Question

Find 'a' if the two polynomials ax³ + 3x² – 9 and 2x³ + 4x + a, leaves the same remainder when divided by x + 3.

Answer 1

The given polynomials are ax³ + 3x² – 9 and 2x³ + 4x + a.

Let p(x) = ax³ + 3x² – 9 and q(x) = 2x³ + 4x + a

Given that p(x) and q(x) leave the same remainder when divided by (x + 3),

Thus by Remainder Theorem, we have

p(–3) = q(–3)

`=>` a(–3)³ + 3(–3)² – 9 = 2(–3)³ + 4(–3) + a 

`=>` –27a + 27 – 9 = –54 – 12 + a

`=>` –27a + 18 = –66 + a

`=>` –27a – a = –66 – 18

`=>` –28a = –84

`=> a = 84/28`

∴ a = 3