Question

So I know that x-2 is not a factor of f(x)=3x^2-10x^2+4x+11, but I don't get why.

Answer 1

do you know how to synthetically divide?

Answer 2

Yes

Answer 3

ok try doing that and let me know what you get- would you like me to set it up for you?

Answer 4

I already did it. I got remainder 163.

Answer 5

i dont think thats the remainder- can you show me what you did?

Answer 6

Oh, I used -2 instead of 2.

Answer 7

So now I got 3

Answer 8

ohh ok so thats where the problem was. the main idea is that if the remainder is 0, then it is a factor, if it is not, then it is not a factor. does that make sense?

Answer 9

You can test to see if something like (x-2) is a factor via the remainder theorem. (x-2) represents a root, r = 2. If 2 is root, then evaluating the polynomial at x = 2 must give you a result of 0. If it does not, then r=2 is not a root and (x-2) is not a factor, because only roots are factors.

Answer 10

Yeah, it does. Thanks! :)

Answer 11

no problem :)