Problems on Remainder theorem

If  2x³ +ax² - 13x + b is divisible by x² -x - 6, then find the value of “a” and “b”.

Answer:

Factorizing x² - x -6 we get,

= x² - 3x + 2x -6

= x(x - 3) + 2(x - 3)

= (x- 3)(x + 2)

if F(x) = 2x³ +ax² - 13x + b

Now according to remainder theorem,  F(3) = 0 and F(-2) = 0 for complete divisibility.

Substituting x = 3 we get

9a + b + 15 = 0     -------------(1)

Similarly substituting x = -2, we get

4a + b + 10 = 0  ---------(2)

Solving Equation 1 and 2 we get,

“a” = -1

“b” = -6