Question

Use the factor theorem to determine whether the first polynomial is a factor of the second polynomial.x+5; x^3 +7x^2+2x-40Is x+5 a factor of x^3 + 7x^2+2x-40? Yes or No

Answer 1

In order to x+5 to be a factor of the other polynomial, the zero of x+5 must also be a zero of the other polynomial.

The zero of x+5 is equal to x = -5.

So, using x = -5 in the other polynomial, we have:

$\begin{gathered} (-5)^3+7\cdot(-5)^2+2\cdot(-5)-40\\ \\ =-125+175-10-40\\ \\ =50-50\\ \\ =0 \end{gathered}$

Since the result is zero, the value x = -5 is a zero of the second polynomial, therefore x+5 is a factor of the second polynomial.

Answer: Yes.