If the polynomials ax 3 +3 x 2 -13 and 2 x 3 -5 x + a when divided by ( x -2) leave the same remainder, find the value of a .

Question

Philoid · Accepted Answer

Let p (x) = ax³+3x²-13 and q (x) = 2x³-5x+a be the given polynomials.

The remainders when p (x) and q (x) are divided by (x – 2) and p (2) and q (2) respectively.

By the given condition, we have:

p (2) = q (2)

a (2)³ + 3 (2)² – 13 = 2 (2)³ – 5 (2) + a

8a + 12 – 13 = 16 – 10 + a

7a – 7 = 0

7a = 7

a =

= 1