Solve (x-4)(x+2)(x^3-10x^2-25x-20)

$$( x - 4 ) ( x + 2 ) ( x ^ { 3 } - 10 x ^ { 2 } - 25 x - 20 )$$

Expand

$$x^{5}-12x^{4}-13x^{3}+110x^{2}+240x+160$$

Solution Steps

Use the distributive property to multiply x-4 by x+2 and combine like terms.

$$\left(x^{2}-2x-8\right)\left(x^{3}-10x^{2}-25x-20\right)$$

Use the distributive property to multiply x^{2}-2x-8 by x^{3}-10x^{2}-25x-20 and combine like terms.

$$x^{5}-12x^{4}-13x^{3}+110x^{2}+240x+160$$

Evaluate

$$\left(x-4\right)\left(x+2\right)\left(x^{3}-10x^{2}-25x-20\right)$$

Solution Steps

Use the distributive property to multiply x-4 by x+2 and combine like terms.

$$\left(x^{2}-2x-8\right)\left(x^{3}-10x^{2}-25x-20\right)$$

Use the distributive property to multiply x^{2}-2x-8 by x^{3}-10x^{2}-25x-20 and combine like terms.

$$x^{5}-12x^{4}-13x^{3}+110x^{2}+240x+160$$