Question

I need help with this practice problem, I’m having trouble finishing this problem I need help answering it

Answer 1

Given the polynomial:

`f(x)=x^3+4x^2+x-6`

Checking randomly to find one root of the given polynomial:

For x = -2;

`\begin{gathered} f(-2)=(-2)^3+4(-2)^2+(-2)-6 \\ f(-2)=0 \end{gathered}`

Hence, -2 is one of the roots of the given polynomial.

Therefore, f(x) can be written as:

`\begin{gathered} f(x)=x^3+4x^2+x-6 \\ f(x)=(x+2)(x^2+2x-3) \\ f(x)=(x+2)(x^2+3x-x-3) \\ f(x)=(x+2)(x(x+3)-1(x+3)) \\ f(x)=(x+2)(x-1)(x+3) \end{gathered}`