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

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

anonymous · Answer

@Directrix ?

anonymous · Answer

Would I be setting the equation to 0?

jiteshmeghwal9 · Answer

By remainder theorem$$f(x)=q(x)(x+3)$$If u put x=-3$$f(-3)=q(-3)(-3+3)$$

directrix · Answer

>>Would I be setting the equation to 0?   Yes

 If (x + 3) is a factor, then x = -3

directrix · Answer

If (x + 3) is a factor and x = -3, then then x = -3 is a zero of the function.

It is also an x-intercept and has coordinates (-3,0).

@Everly  Which option do you think is correct?

anonymous · Answer

Thank you that makes sense and f(0) = -3 seems to make sense to me

directrix · Answer

>> f(0) = -3 

means that if x = 0, then y = -3.

directrix · Answer

We want to get this point:   (-3,0).

directrix · Answer

x = -3, y = 0

anonymous · Answer

Oh f(-3) = 0 ?

directrix · Answer

Yes.

anonymous · Answer

Great! and it makes sense to me too, thank you so much!

jiteshmeghwal9 · Answer

u must know that if (x+a) is a factor of f(x) then

x+a=0=>x=-a is a zero of the function.
f(-a)=0

directrix · Answer

You are welcome.