To determine if x + 8 is a factor of the polynomial f(x) = 2x³ + 17x² + 64, we can use the Factor Theorem. According to this theorem, a polynomial p(x) has a factor of x – c if and only if p(c) = 0.
In our case, since we have x + 8, we will set c = -8. We need to evaluate f(-8):
f(-8) = 2(-8)³ + 17(-8)² + 64Calculating this step-by-step:
- (-8)³ = -512
- 2 * -512 = -1024
- (-8)² = 64
- 17 * 64 = 1088
- f(-8) = -1024 + 1088 + 64
- f(-8) = 128
Since f(-8) = 128, which is not equal to zero, we can conclude that x + 8 is not a factor of the polynomial f(x) = 2x³ + 17x² + 64.