Question

a number a is a root of p(x) if and only if the reminder, when dividing the polynomial by x + a, equals zero, true or false?

Answer 1

True! You can tell because (x - a) is what we can assume to be a factor...if you solve for a: x - a = 0 + a on both sides x = a that is your root. So it will always be the opposite of the number in the parentheses of the factor. You can't always assume something is a factor, but here you can b/c you're looking for a root.

Answer 2

False, it's only true when the polynomial is being divided by x - a.