Question

State if the given binomial is a factor of the given polynomial.Question #9

Answer 1

We can use the Factor Theorem to state if the given binomial is a factor of the given polynomial.

The factor theorem states that when f(c)=0 that means the remainder is zero and (x-c) must be a factor of the polynomial.

The given polynomial is:

`k^3+8k^2+6k-12`

Then if (k+2) is a factor of the polynomial, k+2=0, k=-2, f(-2) must be equal to 0.

Let's check:

`\begin{gathered} f(k)=k^3+8k^2+6k-12 \\ f(-2)=(-2)^3+8(-2)^2+6(-2)-12 \\ f(-2)=-8+8\cdot4-12-12 \\ f(-2)=-8+32-24 \\ f(-2)=32-32 \\ f(-2)=0 \end{gathered}`

Thus, (k+2) is a factor of the given polynomial.