Question

Consider the polynomial P(x)=x³+x²-10x-10. Is x +1 one of the factors of P? Explain.

Answer 1

Yes. See explanation below.

Explanation:

If (x + 1) is a factor of P, this would mean that x +1 = 0, x = -1 is a zero of the equation given by the polynomial.

So we're going to evaluate x = -1 to see if it's a zero

`x^(3)+x^(2)  -10x-10 =(-1)^3+(-1)^2-10(-1)-10= -1+1+10-10=0`

Therefore, when we evaluate x = -1 the polynomial has a result of zero and thus we can conclude that (x +1) is one of the factors of P.