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

a) a = 5, b = 3.

Step-by-step 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.