Question

. 8) A polynomial ax +4x² + 3x-4 and x³-4x+a
when divided by x-3 leaves the same remainder
Find the value of a​

Answer 1

Given ax + 4x^2 + 3x - 4 and x^3 - 4x + a leave the same remainder when divided by x - 3.

Let p(x) = ax+ 4x^2 + 3x - 4 and g(x) = 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,

a(3)+ 4(3)^2 + 3(3) - 4 = (3)^3 - 4(3) + a 3a + 36 + 9 − 4 = 27 − 12 + a. 3a + 41 = 15 + a

2a  = 15 − 41 = − 26

a = -26/2

a=-13

Hope it help you:)

Answer 2

Step-by-step explanation:

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