Question

The polynomial p(x) = x^3 - 4x + a when divided by polynomial (x-3) leaves reminder 5. what is value of a?​

Answer 1

Step-by-step explanation:

Given ax^3 + 4x^2 + 3x - 4 and x^3 -

4x + a leave the same remainder when Let p(x) = ax^3 + 4x^2 + 3x - 4 and g(x) =

divided by x - 3.

x^3 - 4x + a

By remainder theorem, if f(x) is divided by

(x - a) then the remainder is f(a) Here when p(x) and g(x) are divided by (x - 3) the remainders are p(3) and g(3) respectively.

Also given that p(3) = g(3) → (1)

Put x = 3 in both p(x) and g(x) Hence equation (1) becomes, → 27a +36 +9-4-27 - 12 + a → 27a +41 = 15 + a → 26a = 15-41 - 26

a(3)^3 + 4(3)^2 + 3(3) - 4 = (3)^3 - 4(3) + a

:: a = -1

Alternate Method:

According to remainder theorem, if f(x) is divided by (x-a)then remainderis f(a)

f(x) = ax³+4x²+3x-4

g(x)= x³-4x +a

f(3) A(27)+4(9)+3(3)-4

27a+41

g(3)=27-4(3)+a

15+a

f(3)=G(3)

27a+41=15+a 26a=15-41

a=15-41/26

a=-26/26

a=-1

Hope This Helps :)