Question

Question 3 of 21Which values of xwould make a polynomial equal to zero if the factors of thepolynomial were (x+3) and (x+12)?O A. 3 and 12B. -3 and 12O C. -3 and -12O D. 3 and -12SUBMIT

Answer 1

If the factors of a polyomials are

$\begin{gathered} (x+3) \\ (x+12) \end{gathered}$

This means that the polynomial can be written as a power of thouse factors, like:

$P(x)=(x+3)^n(x+12)^m$

As we can see, if either of the factors zeros out, the hole polynomial you be zero too, because anything will be multiplied by zero.

So, to find the values of x that will make this polynomial equal to zero, we just solve the equation of each factor equal to zero.

So, the first possible x value is:

$\begin{gathered} (x+3)=0 \\ x+3=0 \\ x=-3 \end{gathered}$

And the second possible value of x is:

$\begin{gathered} (x+12)=0 \\ x+12=0 \\ x=-12 \end{gathered}$

Thus, the possible values of x that make the polynomial zero are -3 and -12, which corresponds to alternative C.