Question

The remainder of P(X)=6x² + ax? - bx +12 when

divided by g(x) = x +2 is -10 and when divided
by r(x) = x + 1 is 14. What are the values of a
and b?
a) a=5, b=3
b) a=5, b=13
C) a = -31, b = 3
d) a=-31, b=27

Answer 1

a) a = 5, b = 3.

Explanation:

We use the Remainder theorem here:

Lets try a = 5 and b = 3 and when x + 2 is the divisor then P(-2) will be -10:

P(x) = 6x^3 + 5x^2 - 3x + 12

p(-2) = 6(-2)^3 + 5(-2)^2 -3(-2) + 12

= -48 + 20 + 6 + 12

= -48 + 38

= -10.

Also using x + 1 we find that p(-1) = 14 so this is the answer.