Solve (x-1)(x-2)(x-3)/(0-1)(0-2)(0-3)

$$\frac { ( x - 1 ) ( x - 2 ) ( x - 3 ) } { ( 0 - 1 ) ( 0 - 2 ) ( 0 - 3 ) }$$

Evaluate

$$-\frac{\left(x-3\right)\left(x-2\right)\left(x-1\right)}{6}$$

Solution Steps

Subtract 1 from 0 to get -1.

$$\frac{\left(x-1\right)\left(x-2\right)\left(x-3\right)}{-\left(-2\right)\left(-3\right)}$$

Multiply -1 and -2 to get 2.

$$\frac{\left(x-1\right)\left(x-2\right)\left(x-3\right)}{2\left(0-3\right)}$$

Subtract 3 from 0 to get -3.

$$\frac{\left(x-1\right)\left(x-2\right)\left(x-3\right)}{2\left(-3\right)}$$

Multiply 2 and -3 to get -6.

$$\frac{\left(x-1\right)\left(x-2\right)\left(x-3\right)}{-6}$$

Apply the distributive property by multiplying each term of x-1 by each term of x-2.

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

Combine -2x and -x to get -3x.

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

Apply the distributive property by multiplying each term of x^{2}-3x+2 by each term of x-3.

$$\frac{x^{3}-3x^{2}-3x^{2}+9x+2x-6}{-6}$$

Combine -3x^{2} and -3x^{2} to get -6x^{2}.

$$\frac{x^{3}-6x^{2}+9x+2x-6}{-6}$$

Combine 9x and 2x to get 11x.

$$\frac{x^{3}-6x^{2}+11x-6}{-6}$$

Expand

$$-\frac{x^{3}}{6}+x^{2}-\frac{11x}{6}+1$$

Solution Steps

Subtract 1 from 0 to get -1.

$$\frac{\left(x-1\right)\left(x-2\right)\left(x-3\right)}{-\left(-2\right)\left(-3\right)}$$

Multiply -1 and -2 to get 2.

$$\frac{\left(x-1\right)\left(x-2\right)\left(x-3\right)}{2\left(0-3\right)}$$

Subtract 3 from 0 to get -3.

$$\frac{\left(x-1\right)\left(x-2\right)\left(x-3\right)}{2\left(-3\right)}$$

Multiply 2 and -3 to get -6.

$$\frac{\left(x-1\right)\left(x-2\right)\left(x-3\right)}{-6}$$

Apply the distributive property by multiplying each term of x-1 by each term of x-2.

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

Combine -2x and -x to get -3x.

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

Apply the distributive property by multiplying each term of x^{2}-3x+2 by each term of x-3.

$$\frac{x^{3}-3x^{2}-3x^{2}+9x+2x-6}{-6}$$

Combine -3x^{2} and -3x^{2} to get -6x^{2}.

$$\frac{x^{3}-6x^{2}+9x+2x-6}{-6}$$

Combine 9x and 2x to get 11x.

$$\frac{x^{3}-6x^{2}+11x-6}{-6}$$