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?

Question

Mathematics

Merritt

3 January, 15:20

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?

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Milo Fletcher · 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.