Question

If p(x)= 2x3+ a x2+ 3x–3 and f(x) = x3 + x2-4x+ aleave the same remainder when divided by x-2, find the value of a.

answer with working

Answer 1

a = 3

Explanation:

`p(x) = 2x^(3) + ax^(2) +3x -3\\f(x) = x^(3) + x^(2) - 4x + a`

To get the remainder when these polynomials are divided by x - 2, subsitute(x = 2) into both functions.

`p(2) = 2(2^(3)) + a(2^(2)) +(3*2) -3\\p(2) = 19 - 4a\\f(2) = 2^(3) + 2^(2) - (4*2) + a\\f(2) = 4 + a`

Since the remainders are the same, p(2) = f(2)

19 - 4a = 4 + a

19 - 4 = a + 4a

15 = 5a

a = 15/5

a = 3