Question

if the polynomial ax^3+4x^2+3x-4 and x^3-4x+a leave the same remainder when divided by x-3 find the value of a

Answer 1

Step-by-step explanation:

Let p(x) = ax3 + 4x2 + 3x – 4 and q(x) = x3 – 4x + a be the given polynomials.

When p(x) and q(x) are divided by (x – 3) the remainder are p(3) and q(3) respectively.

p(3) = q(3) given

a(3)3 + 4(3)2 + 3 × 3 – 4 = 33 – 4 × 3 + a

⇒ 27a + 36 + 9 – 4 = 27 – 12 + a

⇒ 26a = 15 – 41

⇒ 26a = - 26

∴ a = - 26/26 = - 1