Solve {c}{x^4+x^3-x^2-2x-2}{-(x-1)(x^3-2x)}

$$\left. \begin{array} { c } { x ^ { 4 } + x ^ { 3 } - x ^ { 2 } - 2 x - 2 } \\ { - ( x - 1 ) ( x ^ { 3 } - 2 x ) } \end{array} \right.$$

Evaluate

$$\left(2x+1\right)\left(x^{2}-2\right)$$

Solution Steps

Use the distributive property to multiply x-1 by x^{3}-2x.

$$x^{4}+x^{3}-x^{2}-2x-2-\left(x^{4}-2x^{2}-x^{3}+2x\right)$$

To find the opposite of x^{4}-2x^{2}-x^{3}+2x, find the opposite of each term.

$$x^{4}+x^{3}-x^{2}-2x-2-x^{4}+2x^{2}+x^{3}-2x$$

Combine x^{4} and -x^{4} to get 0.

$$x^{3}-x^{2}-2x-2+2x^{2}+x^{3}-2x$$

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

$$x^{3}+x^{2}-2x-2+x^{3}-2x$$

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

$$2x^{3}+x^{2}-2x-2-2x$$

Combine -2x and -2x to get -4x.

$$2x^{3}+x^{2}-4x-2$$

Expand

$$2x^{3}+x^{2}-4x-2$$

Solution Steps

Use the distributive property to multiply x-1 by x^{3}-2x.

$$x^{4}+x^{3}-x^{2}-2x-2-\left(x^{4}-2x^{2}-x^{3}+2x\right)$$

To find the opposite of x^{4}-2x^{2}-x^{3}+2x, find the opposite of each term.

$$x^{4}+x^{3}-x^{2}-2x-2-x^{4}+2x^{2}+x^{3}-2x$$

Combine x^{4} and -x^{4} to get 0.

$$x^{3}-x^{2}-2x-2+2x^{2}+x^{3}-2x$$

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

$$x^{3}+x^{2}-2x-2+x^{3}-2x$$

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

$$2x^{3}+x^{2}-2x-2-2x$$

Combine -2x and -2x to get -4x.

$$2x^{3}+x^{2}-4x-2$$