A polynomial p(x) leaves remainder 4 when divided by (x − 1) and remainder 10 when divided by (x − 3). What is the remainder when p(x) is divided by (x − 1)(x − 3)?

Question

Accepted Answer

3x + 1. The remainder has the form ax + b. p(1) = a + b = 4 and p(3) = 3a + b = 10, so a = 3 and b = 1: the remainder is 3x + 1.

A polynomial p $(x)$ leaves remainder 4 when divided by $(x - 1)$ and remainder 10 when divided by $(x - 3)$ . What is the remainder when p $(x)$ is divided by $(x - 1) (x - 3)$ ?

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A polynomial p(x) leaves remainder 4 when divided by (x−1) and remainder 10 when divided by (x−3). What is the remainder when p(x) is divided by (x−1)(x−3)?

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Algebra practice

A polynomial p $(x)$ leaves remainder 4 when divided by $(x - 1)$ and remainder 10 when divided by $(x - 3)$ . What is the remainder when p $(x)$ is divided by $(x - 1) (x - 3)$ ?