Question

What must be a factor of the polynomial function fx) graphed on the coordinate plane below?

Answer 1

See in the explanation

Explanation:

Hello! Recall that you need to write complete questions in order to get good and precise answers. However, I'll try to explain this problem in a general way. The definition of polynomial functions states:

$A \ \mathbf{polynomial \ function} \ of \ x \ with \ degree \ n \ is \ given \ by:\\ \\ f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\ldots +a_{2}x^{2}+a_{1}x+a_{0} \\ \\ where \ n \ is \ a \ nonnegative \ integer \ and \ a_{n}, a_{n-1}, \ldots a_{2}, a_{1}, a_{0} \\ with \ a_{n}\neq 0$

Suppose we have the following polynomial function:

$f(x)=x^3+x^2-8x-12$

If $(x-3)$ is a factor of this polynomial function, we can write $f(x)$ as:

$f(x)=\left(ax^2+bx+c\right)\left(x-3\right)$

In whose case:

$f(3)=0$

Evaluating $x=3$

$f(x)=x^3+x^2-8x-12 \\ \\ f(3)=3^3+3^2-8(3)-12 \\ \\ f(3)=27+9-24-12 \\ \\ f(3)=32-32 \\ \\ f(3)=0$

So in conclusion:

$(x-3) \ is \ a \ factor \ of \ f(x)=x^3+x^2-8x-12$

The graph is shown below and is consistent with our conclusion.

Learn more:

Complex zeros: brainly.com/question/13728954

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