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 1

Answer:

a = 3

Step-by-step 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