Question

A number a is a root of P(x) if and only if the remainder, when dividing the polynomial by x - a, equals zero.
A. True
B. 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. Best of luck!

Answer 2

Thank you!