Solve (x+5)(x+1)(x-1/8)(x-3)(x-6)

$$(x+5)(x+1)(x- \frac{ 1 }{ 8 } )(x-3)(x-6)$$

Evaluate

$$\frac{\left(x-6\right)\left(x-3\right)\left(8x-1\right)\left(x+1\right)\left(x+5\right)}{8}$$

Solution Steps

Apply the distributive property by multiplying each term of x+5 by each term of x+1.

$$\left(x^{2}+x+5x+5\right)\left(x-\frac{1}{8}\right)\left(x-3\right)\left(x-6\right)$$

Combine x and 5x to get 6x.

$$\left(x^{2}+6x+5\right)\left(x-\frac{1}{8}\right)\left(x-3\right)\left(x-6\right)$$

Apply the distributive property by multiplying each term of x^{2}+6x+5 by each term of x-\frac{1}{8}.

$$\left(x^{3}+x^{2}\left(-\frac{1}{8}\right)+6x^{2}+6x\left(-\frac{1}{8}\right)+5x+5\left(-\frac{1}{8}\right)\right)\left(x-3\right)\left(x-6\right)$$

Combine x^{2}\left(-\frac{1}{8}\right) and 6x^{2} to get \frac{47}{8}x^{2}.

$$\left(x^{3}+\frac{47}{8}x^{2}+6x\left(-\frac{1}{8}\right)+5x+5\left(-\frac{1}{8}\right)\right)\left(x-3\right)\left(x-6\right)$$

Express 6\left(-\frac{1}{8}\right) as a single fraction.

$$\left(x^{3}+\frac{47}{8}x^{2}+\frac{6\left(-1\right)}{8}x+5x+5\left(-\frac{1}{8}\right)\right)\left(x-3\right)\left(x-6\right)$$

Multiply 6 and -1 to get -6.

$$\left(x^{3}+\frac{47}{8}x^{2}+\frac{-6}{8}x+5x+5\left(-\frac{1}{8}\right)\right)\left(x-3\right)\left(x-6\right)$$

Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.

$$\left(x^{3}+\frac{47}{8}x^{2}-\frac{3}{4}x+5x+5\left(-\frac{1}{8}\right)\right)\left(x-3\right)\left(x-6\right)$$

Combine -\frac{3}{4}x and 5x to get \frac{17}{4}x.

$$\left(x^{3}+\frac{47}{8}x^{2}+\frac{17}{4}x+5\left(-\frac{1}{8}\right)\right)\left(x-3\right)\left(x-6\right)$$

Express 5\left(-\frac{1}{8}\right) as a single fraction.

$$\left(x^{3}+\frac{47}{8}x^{2}+\frac{17}{4}x+\frac{5\left(-1\right)}{8}\right)\left(x-3\right)\left(x-6\right)$$

Multiply 5 and -1 to get -5.

$$\left(x^{3}+\frac{47}{8}x^{2}+\frac{17}{4}x+\frac{-5}{8}\right)\left(x-3\right)\left(x-6\right)$$

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$\left(x^{3}+\frac{47}{8}x^{2}+\frac{17}{4}x-\frac{5}{8}\right)\left(x-3\right)\left(x-6\right)$$

Apply the distributive property by multiplying each term of x^{3}+\frac{47}{8}x^{2}+\frac{17}{4}x-\frac{5}{8} by each term of x-3.

$$\left(x^{4}-3x^{3}+\frac{47}{8}x^{2}x+\frac{47}{8}x^{2}\left(-3\right)+\frac{17}{4}xx+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\left(x^{4}-3x^{3}+\frac{47}{8}x^{3}+\frac{47}{8}x^{2}\left(-3\right)+\frac{17}{4}xx+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Multiply x and x to get x^{2}.

$$\left(x^{4}-3x^{3}+\frac{47}{8}x^{3}+\frac{47}{8}x^{2}\left(-3\right)+\frac{17}{4}x^{2}+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Combine -3x^{3} and \frac{47}{8}x^{3} to get \frac{23}{8}x^{3}.

$$\left(x^{4}+\frac{23}{8}x^{3}+\frac{47}{8}x^{2}\left(-3\right)+\frac{17}{4}x^{2}+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Express \frac{47}{8}\left(-3\right) as a single fraction.

$$\left(x^{4}+\frac{23}{8}x^{3}+\frac{47\left(-3\right)}{8}x^{2}+\frac{17}{4}x^{2}+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Multiply 47 and -3 to get -141.

$$\left(x^{4}+\frac{23}{8}x^{3}+\frac{-141}{8}x^{2}+\frac{17}{4}x^{2}+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Fraction \frac{-141}{8} can be rewritten as -\frac{141}{8} by extracting the negative sign.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{141}{8}x^{2}+\frac{17}{4}x^{2}+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Combine -\frac{141}{8}x^{2} and \frac{17}{4}x^{2} to get -\frac{107}{8}x^{2}.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Express \frac{17}{4}\left(-3\right) as a single fraction.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}+\frac{17\left(-3\right)}{4}x-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Multiply 17 and -3 to get -51.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}+\frac{-51}{4}x-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Fraction \frac{-51}{4} can be rewritten as -\frac{51}{4} by extracting the negative sign.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}-\frac{51}{4}x-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Combine -\frac{51}{4}x and -\frac{5}{8}x to get -\frac{107}{8}x.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}-\frac{107}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Express -\frac{5}{8}\left(-3\right) as a single fraction.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}-\frac{107}{8}x+\frac{-5\left(-3\right)}{8}\right)\left(x-6\right)$$

Multiply -5 and -3 to get 15.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}-\frac{107}{8}x+\frac{15}{8}\right)\left(x-6\right)$$

Apply the distributive property by multiplying each term of x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}-\frac{107}{8}x+\frac{15}{8} by each term of x-6.

$$x^{5}-6x^{4}+\frac{23}{8}x^{3}x+\frac{23}{8}x^{3}\left(-6\right)-\frac{107}{8}x^{2}x-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}xx-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$x^{5}-6x^{4}+\frac{23}{8}x^{4}+\frac{23}{8}x^{3}\left(-6\right)-\frac{107}{8}x^{2}x-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}xx-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{5}-6x^{4}+\frac{23}{8}x^{4}+\frac{23}{8}x^{3}\left(-6\right)-\frac{107}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}xx-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Multiply x and x to get x^{2}.

$$x^{5}-6x^{4}+\frac{23}{8}x^{4}+\frac{23}{8}x^{3}\left(-6\right)-\frac{107}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Combine -6x^{4} and \frac{23}{8}x^{4} to get -\frac{25}{8}x^{4}.

$$x^{5}-\frac{25}{8}x^{4}+\frac{23}{8}x^{3}\left(-6\right)-\frac{107}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Express \frac{23}{8}\left(-6\right) as a single fraction.

$$x^{5}-\frac{25}{8}x^{4}+\frac{23\left(-6\right)}{8}x^{3}-\frac{107}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Multiply 23 and -6 to get -138.

$$x^{5}-\frac{25}{8}x^{4}+\frac{-138}{8}x^{3}-\frac{107}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Reduce the fraction \frac{-138}{8} to lowest terms by extracting and canceling out 2.

$$x^{5}-\frac{25}{8}x^{4}-\frac{69}{4}x^{3}-\frac{107}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Combine -\frac{69}{4}x^{3} and -\frac{107}{8}x^{3} to get -\frac{245}{8}x^{3}.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Express -\frac{107}{8}\left(-6\right) as a single fraction.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{-107\left(-6\right)}{8}x^{2}-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Multiply -107 and -6 to get 642.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{642}{8}x^{2}-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Reduce the fraction \frac{642}{8} to lowest terms by extracting and canceling out 2.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{321}{4}x^{2}-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Combine \frac{321}{4}x^{2} and -\frac{107}{8}x^{2} to get \frac{535}{8}x^{2}.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Express -\frac{107}{8}\left(-6\right) as a single fraction.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{-107\left(-6\right)}{8}x+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Multiply -107 and -6 to get 642.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{642}{8}x+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Reduce the fraction \frac{642}{8} to lowest terms by extracting and canceling out 2.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{321}{4}x+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Combine \frac{321}{4}x and \frac{15}{8}x to get \frac{657}{8}x.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{657}{8}x+\frac{15}{8}\left(-6\right)$$

Express \frac{15}{8}\left(-6\right) as a single fraction.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{657}{8}x+\frac{15\left(-6\right)}{8}$$

Multiply 15 and -6 to get -90.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{657}{8}x+\frac{-90}{8}$$

Reduce the fraction \frac{-90}{8} to lowest terms by extracting and canceling out 2.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{657}{8}x-\frac{45}{4}$$

Expand

$$x^{5}-\frac{25x^{4}}{8}-\frac{245x^{3}}{8}+\frac{535x^{2}}{8}+\frac{657x}{8}-\frac{45}{4}$$

Solution Steps

Apply the distributive property by multiplying each term of x+5 by each term of x+1.

$$\left(x^{2}+x+5x+5\right)\left(x-\frac{1}{8}\right)\left(x-3\right)\left(x-6\right)$$

Combine x and 5x to get 6x.

$$\left(x^{2}+6x+5\right)\left(x-\frac{1}{8}\right)\left(x-3\right)\left(x-6\right)$$

Apply the distributive property by multiplying each term of x^{2}+6x+5 by each term of x-\frac{1}{8}.

$$\left(x^{3}+x^{2}\left(-\frac{1}{8}\right)+6x^{2}+6x\left(-\frac{1}{8}\right)+5x+5\left(-\frac{1}{8}\right)\right)\left(x-3\right)\left(x-6\right)$$

Combine x^{2}\left(-\frac{1}{8}\right) and 6x^{2} to get \frac{47}{8}x^{2}.

$$\left(x^{3}+\frac{47}{8}x^{2}+6x\left(-\frac{1}{8}\right)+5x+5\left(-\frac{1}{8}\right)\right)\left(x-3\right)\left(x-6\right)$$

Express 6\left(-\frac{1}{8}\right) as a single fraction.

$$\left(x^{3}+\frac{47}{8}x^{2}+\frac{6\left(-1\right)}{8}x+5x+5\left(-\frac{1}{8}\right)\right)\left(x-3\right)\left(x-6\right)$$

Multiply 6 and -1 to get -6.

$$\left(x^{3}+\frac{47}{8}x^{2}+\frac{-6}{8}x+5x+5\left(-\frac{1}{8}\right)\right)\left(x-3\right)\left(x-6\right)$$

Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.

$$\left(x^{3}+\frac{47}{8}x^{2}-\frac{3}{4}x+5x+5\left(-\frac{1}{8}\right)\right)\left(x-3\right)\left(x-6\right)$$

Combine -\frac{3}{4}x and 5x to get \frac{17}{4}x.

$$\left(x^{3}+\frac{47}{8}x^{2}+\frac{17}{4}x+5\left(-\frac{1}{8}\right)\right)\left(x-3\right)\left(x-6\right)$$

Express 5\left(-\frac{1}{8}\right) as a single fraction.

$$\left(x^{3}+\frac{47}{8}x^{2}+\frac{17}{4}x+\frac{5\left(-1\right)}{8}\right)\left(x-3\right)\left(x-6\right)$$

Multiply 5 and -1 to get -5.

$$\left(x^{3}+\frac{47}{8}x^{2}+\frac{17}{4}x+\frac{-5}{8}\right)\left(x-3\right)\left(x-6\right)$$

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$\left(x^{3}+\frac{47}{8}x^{2}+\frac{17}{4}x-\frac{5}{8}\right)\left(x-3\right)\left(x-6\right)$$

Apply the distributive property by multiplying each term of x^{3}+\frac{47}{8}x^{2}+\frac{17}{4}x-\frac{5}{8} by each term of x-3.

$$\left(x^{4}-3x^{3}+\frac{47}{8}x^{2}x+\frac{47}{8}x^{2}\left(-3\right)+\frac{17}{4}xx+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\left(x^{4}-3x^{3}+\frac{47}{8}x^{3}+\frac{47}{8}x^{2}\left(-3\right)+\frac{17}{4}xx+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Multiply x and x to get x^{2}.

$$\left(x^{4}-3x^{3}+\frac{47}{8}x^{3}+\frac{47}{8}x^{2}\left(-3\right)+\frac{17}{4}x^{2}+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Combine -3x^{3} and \frac{47}{8}x^{3} to get \frac{23}{8}x^{3}.

$$\left(x^{4}+\frac{23}{8}x^{3}+\frac{47}{8}x^{2}\left(-3\right)+\frac{17}{4}x^{2}+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Express \frac{47}{8}\left(-3\right) as a single fraction.

$$\left(x^{4}+\frac{23}{8}x^{3}+\frac{47\left(-3\right)}{8}x^{2}+\frac{17}{4}x^{2}+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Multiply 47 and -3 to get -141.

$$\left(x^{4}+\frac{23}{8}x^{3}+\frac{-141}{8}x^{2}+\frac{17}{4}x^{2}+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Fraction \frac{-141}{8} can be rewritten as -\frac{141}{8} by extracting the negative sign.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{141}{8}x^{2}+\frac{17}{4}x^{2}+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Combine -\frac{141}{8}x^{2} and \frac{17}{4}x^{2} to get -\frac{107}{8}x^{2}.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}+\frac{17}{4}x\left(-3\right)-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Express \frac{17}{4}\left(-3\right) as a single fraction.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}+\frac{17\left(-3\right)}{4}x-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Multiply 17 and -3 to get -51.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}+\frac{-51}{4}x-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Fraction \frac{-51}{4} can be rewritten as -\frac{51}{4} by extracting the negative sign.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}-\frac{51}{4}x-\frac{5}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Combine -\frac{51}{4}x and -\frac{5}{8}x to get -\frac{107}{8}x.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}-\frac{107}{8}x-\frac{5}{8}\left(-3\right)\right)\left(x-6\right)$$

Express -\frac{5}{8}\left(-3\right) as a single fraction.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}-\frac{107}{8}x+\frac{-5\left(-3\right)}{8}\right)\left(x-6\right)$$

Multiply -5 and -3 to get 15.

$$\left(x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}-\frac{107}{8}x+\frac{15}{8}\right)\left(x-6\right)$$

Apply the distributive property by multiplying each term of x^{4}+\frac{23}{8}x^{3}-\frac{107}{8}x^{2}-\frac{107}{8}x+\frac{15}{8} by each term of x-6.

$$x^{5}-6x^{4}+\frac{23}{8}x^{3}x+\frac{23}{8}x^{3}\left(-6\right)-\frac{107}{8}x^{2}x-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}xx-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$x^{5}-6x^{4}+\frac{23}{8}x^{4}+\frac{23}{8}x^{3}\left(-6\right)-\frac{107}{8}x^{2}x-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}xx-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$x^{5}-6x^{4}+\frac{23}{8}x^{4}+\frac{23}{8}x^{3}\left(-6\right)-\frac{107}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}xx-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Multiply x and x to get x^{2}.

$$x^{5}-6x^{4}+\frac{23}{8}x^{4}+\frac{23}{8}x^{3}\left(-6\right)-\frac{107}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Combine -6x^{4} and \frac{23}{8}x^{4} to get -\frac{25}{8}x^{4}.

$$x^{5}-\frac{25}{8}x^{4}+\frac{23}{8}x^{3}\left(-6\right)-\frac{107}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Express \frac{23}{8}\left(-6\right) as a single fraction.

$$x^{5}-\frac{25}{8}x^{4}+\frac{23\left(-6\right)}{8}x^{3}-\frac{107}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Multiply 23 and -6 to get -138.

$$x^{5}-\frac{25}{8}x^{4}+\frac{-138}{8}x^{3}-\frac{107}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Reduce the fraction \frac{-138}{8} to lowest terms by extracting and canceling out 2.

$$x^{5}-\frac{25}{8}x^{4}-\frac{69}{4}x^{3}-\frac{107}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Combine -\frac{69}{4}x^{3} and -\frac{107}{8}x^{3} to get -\frac{245}{8}x^{3}.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}-\frac{107}{8}x^{2}\left(-6\right)-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Express -\frac{107}{8}\left(-6\right) as a single fraction.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{-107\left(-6\right)}{8}x^{2}-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Multiply -107 and -6 to get 642.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{642}{8}x^{2}-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Reduce the fraction \frac{642}{8} to lowest terms by extracting and canceling out 2.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{321}{4}x^{2}-\frac{107}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Combine \frac{321}{4}x^{2} and -\frac{107}{8}x^{2} to get \frac{535}{8}x^{2}.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}-\frac{107}{8}x\left(-6\right)+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Express -\frac{107}{8}\left(-6\right) as a single fraction.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{-107\left(-6\right)}{8}x+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Multiply -107 and -6 to get 642.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{642}{8}x+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Reduce the fraction \frac{642}{8} to lowest terms by extracting and canceling out 2.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{321}{4}x+\frac{15}{8}x+\frac{15}{8}\left(-6\right)$$

Combine \frac{321}{4}x and \frac{15}{8}x to get \frac{657}{8}x.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{657}{8}x+\frac{15}{8}\left(-6\right)$$

Express \frac{15}{8}\left(-6\right) as a single fraction.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{657}{8}x+\frac{15\left(-6\right)}{8}$$

Multiply 15 and -6 to get -90.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{657}{8}x+\frac{-90}{8}$$

Reduce the fraction \frac{-90}{8} to lowest terms by extracting and canceling out 2.

$$x^{5}-\frac{25}{8}x^{4}-\frac{245}{8}x^{3}+\frac{535}{8}x^{2}+\frac{657}{8}x-\frac{45}{4}$$