Which of the following best describe the relationship between the binomial (x-3) and the polynomial Fx=2x^2-3x+3?

Question

mathmale · Answer

Good morning!

Please write that function as F(x).   F(x) = 2x^2 - 3x + 3.  Immediately I'd be curious whether or not x-3 is a factor of that polynomial.

So I'd try dividing x-3 into F(x) (using long division), or
I'd obtain the possible root x = 3 from (x-3)=0 and use 3 as the divisor in synthetic division.  In either case you will either get a remainder or not get a remainder.  If there's no remainder, you can safely conclude that (x-3) is a factor of the given polynomial F(x).

anonymous · Answer

It's not a factor

mathmale · Answer

Mind explaining how you arrived at that conclusion?

mathmale · Answer

In the case of a problem such as the one  you've posted here, your "answer" should always include justification.