Question

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?

Answer 1

a = 11, b = -60.

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.