Question

By the Remainder Theorem, what can be said about the polynomial function w(x) if w(−5)=3 ?

the remainder must be _________ when w(x) is divided by _________


thanks so much!

Answer 1

well, ding ding ding!! let's recall the remainder's theorem

if some function f(x) has a factor of say x - a, then if we plug the "a" in f(x) what we get is the remainder, that is, the remainder in a division of f(x) by (x-a).

all that mouthful said, well, since we know of w(-5), that means w(x) must have a factor of x - (-5) or namely x + 5.

we also know that w(-5) = 3, well, that means that 3 is the remainder of such division, that is, w(x) ÷ (x + 5), gives us a remainder of 3.