Question

Using the inspection method, what constant term must the numerator of the rational expression x2+8x+11x+6 have so (x + 6) is one of its factors?

For the numerator to have (x + 6) as a factor, its constant term must be

Answer 1

here is my next question...not multiple choice, will give medal

Answer 2

If (x + 6) is a factor it implies if we put x = -6, f(x) should be zero.
f(x) = x^2+8x+11x+6
f(-6) = ?

Answer 3

so now, we are looking for f....what's the best way to find it?

Answer 4

Can you post a link of this question as well?
I am wondering why they have it as 8x + 11x instead of 19x.

Answer 5

can you see that okay?

Answer 6

that would make a lot of sense....sorry.

Answer 7

Yeah, I think you made a mistake in typing the problem.
The rational expression is x^2 + 8x + 11 NOT x^2 + 8x + 11x + 6

Answer 8

f(x) = x^2 + 8x + 11
If (x + 6) is a factor, then putting x = -6 should make f(x) = 0
f(-6) = (-6)^2 + 8(-6) + 11
= 36 - 48 + 11 = -1
We are left with -1 instead of zero.
Therefore, we need to increase f(x) by 1 to get f(-6) to equal zero.
So f(x) should be x^2 + 8x + 12
So the CONSTANT term should be 12 in order for (x + 6) to be a factor.

Answer 9

sorry i just wrote all of that out because i want to actually learn something:) haha thank you. i do understand how you got that answer now. would you be able to keep helping me?

Answer 10

i could put the new problem up sothat i can give you another medal:)

Answer 11

@aum

Answer 12

close this one. post a new one and tag me and I will try to help.

Answer 13

:) thank you