Question

Which values of x would make a polynomial equal to zero iſ the factors of thepolynomial were (x-3) and (x-7)?

Answer 1

ANSWER

3 and 7

EXPLANATION

If the factors are (x-3) and (x-7), we can write the polynomial as the product of its factors:

$P(x)=(x-3)(x-7)(\ldots)$

(...) is if this polynomial had more factors.

This is a product, so if any of the factors of the product is zero then the whole product is zero:

$(x-3)(x-7)(\ldots)=0$

We know two of the factors, so to make the polynomial zero we have:

$\begin{gathered} x-3=0 \\ x=3 \\ \text{ or} \\ x-7=0 \\ x=7 \end{gathered}$

Therefore, two of the values that make this polynomial zero are 3 and 7.