Question

Select the correct answer. Which expression is a factor of this polynomial?

Answer 1

SOLUTION:

We are to find the expression that is a factor of the given polynomial.

$x^3+2x^2-9x\text{ -18}$

We try all the given options by substituting the value of x after equating it to zero and any of the options that gives zero is a factor.

Trying option ( x + 2);

$\begin{gathered} x\text{ + 2 = 0} \\ x\text{ = -2} \end{gathered}$

We now substitute, x = -2 into the given polynomial.

$\begin{gathered} x^3+2x^2-9x\text{ -18} \\ (-2)^3+2(-2)^2\text{ - 9(-2) -18} \\ -8\text{ + 8 + 18 -18 }=\text{ 0} \\ \end{gathered}$

Since the result gives zero, so ( x + 2 ) is a factor of the given polynomial.