# Polynomials bx2 + x + 5 and bx3 – 2x + 5 are divided by polynomial x – 3 and the remainders are and respectively. If m – n =0 then find the value of b.

Put x = 3 in the first polynomial:

b× (3)2 + 3 + 5 = m

9b + 8 = m ………………………………….. (i)

Put x = 3 in the second polynomial

b× (3)3 -2× 3 + 5 = n

27b -6 + 5 = n

27b -1 = n …………………………………. (ii)

Equation (i) – (ii)

m –n = 9b + 8 – (27b -1)

but m-n = 0

9b + 8 -27b + 1 = 0

-18b + 9 = 0

18b = 9

b = 9/18

b = 1/2

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