Question

What are the zeros of the polynomial functionF(x) = x³ + x² - 6x?OA.x = -2, x = 0, and x = 3B. x = -6, x = 0, and x = 1C. x = -1, x = 0, and x = 6OD. x = -3, x = 0, and x = 2

Answer 1

Given the polynomial functions:

$F(x)=x^3+x^2-6x$

We can express this polynomial in factored form:

$F(x)=x(x^2+x-6)$

But:

$x^2+x-6=(x+3)(x-2)$

Then:

$F(x)=x(x+3)(x-2)$

Finally, to find the zeros of the polynomial, we solve the equation:

$x(x+3)(x-2)=0$

This cubic equation turns into three linear equations:

$\begin{gathered} x=0 \\ x+3=0\Rightarrow x=-3 \\ x-2=0\Rightarrow x=2 \end{gathered}$

Answer:

$D.\text{ }x=-3,x=0,x=2$