If the polynomials ax 3 + 4x 2 -3x - 4 and x 3 - 4x + a leave the same remainder when divided by (x - 3). Then, what is the value of a?

Q: If the polynomials ax 3 + 4x 2 -3x - 4 and x 3 - 4x + a leave the same remainder when divided by (x - 3). Then, what is the value of a?

Since, p(x) = ax3 + 4x2 + 3x - 4 and q(x) = x3 -4x + a divided by x - 3, hence p(3) = q(3) ⇒ a x 33 + 4 x 32 + 3 x 3 - 4 = 33 - 4 x 3 + a ∴ a = -1

2
-1
3
4

Correct Answer: -1

Explanation:

Since, p(x) = ax³ + 4x² + 3x - 4 and q(x) = x³ -4x + a divided by x - 3, hence p(3) = q(3)
⇒ a x 3³ + 4 x 3² + 3 x 3 - 4 = 3³ - 4 x 3 + a
∴ a = -1

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