Question

Medal and a fan!!! PLZ HELP!
Given a polynomial f(x), if (x + 7) is a factor, what else must be true?

Answer 1

f(0) = 7

f(0) = -7

f(-7) = 0

f(7) = 0

Answer 2

kk i can help you

Answer 3

we know that what ever we get it has to be added with 7.

Answer 4

if you picked D you get f(7) but once you add that 7 with 7 it will not equal 0.

Answer 5

if you pick B 0+7 will be 7 not -7 so B isn't it either.

Answer 6

so the answer is c?

Answer 7

what confuses me is A and C are both true...

Answer 8

but i didnt figure it out...

Answer 9

its ok

Answer 10

@vineeth10
It is a known property of polynomials that when a polynomial p(x) is divided by (x-k), the remainder equals p(k).

Answer 11

For example, we know that \(p(x)=(x^2+3x+2)=(x+1)(x+2)\), so (x+1) and (x+2) are factors of p(x). This in turn means that p(-1)=0, and p(-2)=0.

Answer 12

@mathmate or anyone
The options are:f(0) = 7

f(0) = -7

f(-7) = 0

f(7) = 0

Answer 13

If (x + 7) is a factor of f(x) it means, f(x) can be written as follows:
f(x) = (x+7) * (some other factor)

If I put x = -7 above, I will get:

f(-7) = (-7 + 7) * (some other factor)
f(-7) = 0 * (some other factor)
f(-7) = 0

Answer 14

Thanks!!! amu

Answer 15

yw.