Determine if x - c is A Factor...1

College Algebra
Chapter 1/Section 6

Use synthetic division to determine if x - c is a factor of the given polynomial.

 

If we divide a polynomial f(x) by (x - c), and (x - c) is a factor of the polynomial f(x), then the remainder of that division is simply equal to 0. Thus, according to this theorem, if the remainder of a division like those described above equals zero, (x - c) must be a factor.

 

The remainder here is not zero. This means my work is wrong.

 

your work is good
-4 x^3 + 5 x^2 + 8 = (-4 x^2 + 17 x - 51)(x + 3) + 161

so, the remainder of that division is 161, which means (x + 3) is not a factor

 

I totally get it. The remainder must be 0 for (x - c) to be a factor of f(x).