Question

The polynimials 2x^3 − 7x^2 + ax – 6 and x^3 − 8x^2 + (2a + 1) x – 16 leave the same remainder when divided by x – 2. Find the value of ‘a’

Answer 1

2 x cube minus 7 x square + aX - 6
x cube minus 8 x square + (2A + 1 ) x minus 16

2(2)^3 - 7(2)^2 + a(2) - 6
16 - 28 + 2a - 6
-18 + 2a

2(2)^3 - 8(2)^2 + (2a + 1)2 -16
-24 -16 +2 +4a
-38 + 4a

-18 + 38 = 4a - 2a
2a = 20
a =10