Question

Assertion (A): When a polynomial $$f(x)$$ is divided by $$(3x + 4)$$, then the remainder is $$f\left(-\frac{3}{4}\right)$$.

Reason (R): Remainder theorem states that when a polynomial $$f(x)$$ is divided by $$(x - \alpha)$$, then the remainder is $$f(\alpha)$$.

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

A is false, but R is true.

Explanation:

Since $$3x + 4 = 3\left(x + \frac{4}{3}\right)$$, the remainder on division is $$f\left(-\frac{4}{3}\right)$$, not $$f\left(-\frac{3}{4}\right)$$. So A is false, while R is the correct remainder theorem.