Question

Select all polynomials that have (x+2) as a factor. A(x) = x^3 - 3x^2 - 10xB(x) = x^3 + 5x^2 + 4xC(x) = x^3 - 2x^2 - 13x - 10D(x) = x^3 - 6x^2 + 11x - 6

Answer 1

ANSWER

$\begin{gathered} A\mleft(x\mright)=x^3-3x^2-10x \\ C\mleft(x\mright)=x^3-2x^2-13x-10 \end{gathered}$

EXPLANATION

We want to find which of the given polynomials has (x + 2) as a factor.

To do this, we have to equate (x + 2) to 0 and solve for x:

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

Now, substitute that into each of the polynomials. If (x + 2) is a factor of a polynomial, the polynomial will become 0 after the substitution is made.

Therefore, for A(x), we have:

$\begin{gathered} A(-2)=(-2)^3-3(-2)^2-10(-2) \\ A(-2)=-8-12+20 \\ A(-2)=0 \end{gathered}$

For B(x), we have:

$\begin{gathered} B(-2)=(-2)^3+5(-2)^2+4(-2) \\ B(-2)=-8+20-8 \\ B(-2)=4 \end{gathered}$

For C(x), we have:

$\begin{gathered} C(-2)=(-2)^3-2(-2)^2-13(-2)-10 \\ C(-2)=-8-8+26-10 \\ C(-2)=0 \end{gathered}$

For D(x), we have:

$\begin{gathered} D(-2)=(-2)^3-6(-2)^2+11(-2)-6 \\ D(-2)=-8-24-22-6 \\ D(-2)=-60 \end{gathered}$

Therefore, the polynomials that have (x + 2) as a factor are polynomials A(x) and C(x).