Solve 4x^5-3x^2+x-5+(-x^2+4x-3)(x-8)

$$4 x ^ { 5 } - 3 x ^ { 2 } + x - 5 + ( - x ^ { 2 } + 4 x - 3 ) ( x - 8 )$$

Evaluate

$$4x^{5}-x^{3}+9x^{2}-34x+19$$

Solution Steps

Use the distributive property to multiply -x^{2}+4x-3 by x-8 and combine like terms.

$$4x^{5}-3x^{2}+x-5+\left(-x^{2}\right)x-8\left(-x^{2}\right)+4x^{2}-35x+24$$

Multiply -8 and -1 to get 8.

$$4x^{5}-3x^{2}+x-5+\left(-x^{2}\right)x+8x^{2}+4x^{2}-35x+24$$

Combine 8x^{2} and 4x^{2} to get 12x^{2}.

$$4x^{5}-3x^{2}+x-5+\left(-x^{2}\right)x+12x^{2}-35x+24$$

Combine -3x^{2} and 12x^{2} to get 9x^{2}.

$$4x^{5}+9x^{2}+x-5+\left(-x^{2}\right)x-35x+24$$

Combine x and -35x to get -34x.

$$4x^{5}+9x^{2}-34x-5+\left(-x^{2}\right)x+24$$

Add -5 and 24 to get 19.

$$4x^{5}+9x^{2}-34x+19+\left(-x^{2}\right)x$$

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

$$4x^{5}+9x^{2}-34x+19-x^{3}$$

Expand

$$4x^{5}-x^{3}+9x^{2}-34x+19$$

Solution Steps

Use the distributive property to multiply -x^{2}+4x-3 by x-8 and combine like terms.

$$4x^{5}-3x^{2}+x-5+\left(-x^{2}\right)x-8\left(-x^{2}\right)+4x^{2}-35x+24$$

Multiply -8 and -1 to get 8.

$$4x^{5}-3x^{2}+x-5+\left(-x^{2}\right)x+8x^{2}+4x^{2}-35x+24$$

Combine 8x^{2} and 4x^{2} to get 12x^{2}.

$$4x^{5}-3x^{2}+x-5+\left(-x^{2}\right)x+12x^{2}-35x+24$$

Combine -3x^{2} and 12x^{2} to get 9x^{2}.

$$4x^{5}+9x^{2}+x-5+\left(-x^{2}\right)x-35x+24$$

Combine x and -35x to get -34x.

$$4x^{5}+9x^{2}-34x-5+\left(-x^{2}\right)x+24$$

Add -5 and 24 to get 19.

$$4x^{5}+9x^{2}-34x+19+\left(-x^{2}\right)x$$

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

$$4x^{5}+9x^{2}-34x+19-x^{3}$$