Question

Find a cubic function with the given zeros-2,5,-6Answer choices: f(x)= x^3 + 3x^2 + 28x - 60f(x)= x^3 - 3x^2 - 28x - 60f(x)= x^3 + 3x^2 - 28x -60f(x)= x^3 + 3x^2 - 28x + 60

Answer 1

The roots of the polynomial function are x=-2, x=5 and x=-6

You can express them as

(x+2)(x-5)(x+6)=0

To reach the cubic function you have to expand this expression.

Apply the distributive propperty of multiplications to solve.

First multiply the first two parentheses:

$\begin{gathered} (x+2)(x-5)=x^2-5x+2x-10 \\ x^2-3x-10 \end{gathered}$

Next multiply this result to the third parentheses:

$\begin{gathered} (x^2-3x-10)(x+6)=x^3+6x^2-3x^2-18x-10x-60\text{ \rightarrow{}Symplify} \\ x^3+3x^2-28x-60 \end{gathered}$

The solution is the third option.

$f(x)=x^3+3x^2-28x-60$