select all polynomials that have (x + 2) as a factor. choose all answers that apply: a a(x)=x^3 - 3x^2 - 10x…

select all polynomials that have (x + 2) as a factor. choose all answers that apply: a a(x)=x^3 - 3x^2 - 10x b b(x)=x^3 + 5x^2 + 4x c c(x)=x^3 - 2x^2 - 13x - 10 d d(x)=x^3 - 6x^2 + 11x - 6

select all polynomials that have (x + 2) as a factor. choose all answers that apply: a a(x)=x^3 - 3x^2 - 10x b b(x)=x^3 + 5x^2 + 4x c c(x)=x^3 - 2x^2 - 13x - 10 d d(x)=x^3 - 6x^2 + 11x - 6

Answer

Explanation:

Step1: Use the factor - theorem

According to the factor - theorem, if ((x + 2)) is a factor of a polynomial (P(x)), then (P(-2)=0).

Step2: Evaluate (A(x)) at (x = - 2)

[ \begin{align*} A(-2)&=(-2)^{3}-3(-2)^{2}-10(-2)\ &=-8 - 3\times4+20\ &=-8 - 12 + 20\ &=0 \end{align*} ]

Step3: Evaluate (B(x)) at (x=-2)

[ \begin{align*} B(-2)&=(-2)^{3}+5(-2)^{2}+4(-2)\ &=-8 + 5\times4-8\ &=-8 + 20-8\ &=4\neq0 \end{align*} ]

Step4: Evaluate (C(x)) at (x = - 2)

[ \begin{align*} C(-2)&=(-2)^{3}-2(-2)^{2}-13(-2)-10\ &=-8-2\times4 + 26-10\ &=-8-8 + 26-10\ &=0 \end{align*} ]

Step5: Evaluate (D(x)) at (x=-2)

[ \begin{align*} D(-2)&=(-2)^{3}-6(-2)^{2}+11(-2)-6\ &=-8-6\times4-22 - 6\ &=-8-24-22 - 6\ &=-60\neq0 \end{align*} ]

Answer:

A. (A(x)=x^{3}-3x^{2}-10x), C. (C(x)=x^{3}-2x^{2}-13x - 10)