Question

Everyone needs to get off of social and help us -_-

The volume of a rectangular prism is represented by the function x3 + 9x2 + 6x − 16. The length of the box is x + 2, while the height is x + 8. Find the expression representing the width of the box.
x − 4
x − 1
x + 1
x + 4

Answer 1

(x+2)(x+8)(x+k)=x^3+9x^2+6x-16

(x^2+10x+16)(x+k)=x^3+9x^2+6x-16

x^3+10x^2+16x+kx^2+10kx+16k=x^3+9x^2+6x-16

kx^2+10kx+16k=-x^2-10x-16

k(x^2+10x+16)=-x^2-10x-16

k=(-x^2-10x-16)/(x^2+10x+16)

k=-1

so the width is (x-1)