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$a x^{3} + b x^{2} + x - 6$ has $(x + 2)$ as a factor and leaves remainder 36 when divided by $(x - 2)$ . Find a and $b$ .

Competition practiceAlgebra

A $a = 6, b = 2$
B $a = 2, b = 6$
C $a = 2, b = - 6$
D $a = 4, b = 2$

Step-by-Step Solution

p (- 2) = - 8 a + 4 b - 8 = 0

gives

b - 2 a = 2

;

p (2) = 8 a + 4 b - 4 = 36

gives

2 a + b = 10

. So

a = 2, b = 6

.

Answer: B)

a = 2, b = 6

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