Question

The volume​ V(x) of a box in terms of its height x is given by the function

Upper V left parenthesis x right parenthesis equals x cubed plus 4 x squared minus 5 xV(x)=x3+4x2−5x.

Factor the expression for​ V(x).​

Answer 1

Factor of the expression for​  $V(x)=x^3+4x^2-5x$ is  $V(x)=x(x-1)(x+5)$

Step-by-step explanation:

Here we have , The volume​ V(x) of a box in terms of its height x is given by the function  Upper V left parenthesis x right parenthesis equals x cubed plus 4 x squared minus 5x V(x)=x3+4x2−5x. We need to Factor the expression for​ V(x).​ Let's find out:

We have following expression as : $V(x)=x^3+4x^2-5x$

⇒ $V(x)=x^3+4x^2-5x$

⇒ $V(x)=x(x^2+4x-5)$

⇒ $V(x)=x(x^2+5x-x-5)$

⇒ $V(x)=x(x(x+5)-x-5)$

⇒ $V(x)=x(x(x+5)-1(x+5))$

⇒ $V(x)=x(x-1)(x+5)$

Therefore , Factor of the expression for​  $V(x)=x^3+4x^2-5x$ is  $V(x)=x(x-1)(x+5)$ .