Given a polynomial f(x), if (x + 3) is a factor, what else must be true?

f(3) = 0
f(-3) = 0
f(0) = 3
f(0) = -3

@jim_thompson5910

Question

Given a polynomial f(x), if (x + 3) is a factor, what else must be true?

        f(3) = 0
	f(-3) = 0
	f(0) = 3
	f(0) = -3

@jim_thompson5910

jim_thompson5910 · Answer

what did you get so far on it?

marcon · Answer

I think I have to use the zero product property to figure it out

diamondboy · Answer

d factor of d function is -3 right?

jim_thompson5910 · Answer

how would you use the zero product property?

marcon · Answer

Thats what I need help on @jim

marcon · Answer

Actually I'm not sure, we probably don't need to use the zero product property... I'm just confused on how to do this in general. Can you guys help me with the steps?

jim_thompson5910 · Answer

ok let's say we had (x+3)(x-5) = 0

you would use the zero product property to get x+3 = 0 or x-5 = 0. Agreed?

marcon · Answer

mmhmm

marcon · Answer

What do we do next?

marcon · Answer

f(x) = (x + 3)
      = -3
f(-3) = 0     <-------- Correct?             @jim_thompson5910

marcon · Answer

@Michele_Laino

jim_thompson5910 · Answer

yes correct, if x+3 is a factor, then x = -3 is a root

so f(-3) = 0

marcon · Answer

Thank you :D

jim_thompson5910 · Answer

no problem