If (x+4) and (x-3) are the facters of the

polynomial

X^3 + ax^2 - 2 (x-b)

What must be the values of a and b?

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.