Answer:
a = 11, b = -60.
Step-by-step explanation:
If x + 4 and x - 3 are factors then , by the Factor Theorem, f(-4) = 0 and f(3) = 0.
So we have:
(-4)^3 + (-4)^2a - 2(-4 - b) = 0 and
(3)^3 + (3)^2a - 2(3 - b) = 0
Simplifying:
-64 + 16a + 8 + 2b = 0
27 + 9a - 6 + 2b = 0
16a + 2b = 56
9a + 2b = -21 Subtracting theses last 2 equations:
7a = 77
a = 11
Substituting to get the value of b:
16*11 + 2b = 56
2b = 56 - 176
2b = -120
b = -60.
