determine if -4 is a zero

Question

Determine whether x = –4 is a zero of the polynomial

f(x) = x^3 – 2x^2 – 5x + 6

Answer 1

To determine whether -4 is a zero of f(x), we simply have to evaluate f(-4) and if it equals zero, then x=-4 is a zero of f(x)!

Answer 2

Using synthetic division, if you get a remainder of 0, the -4 is a factor

-4 | 1 -2 -5 6

-4 24 -76

1 -6 19 -70

The remainder is -70, not zero. So -4 is not a factor of this polynomial.