Question

If an unknown polynomial is divided by (x – 1) and (x – 2) we

obtain the remainder 2 and 1 respectively, then the remainder resulting from the division of this polynomial by

(x – 1) (x – 2) is –

• A. 3
• B. – 3
• C. 3 – x
• D. 3 – 2x

Answer 1

Answer: (C)

3 – x

Answer 2

The polynomial be P(x), when divided by

(x – 1) leaves remainded 2 ⇒ P(1) = 2 and, when P(x) divided

by (x – 2) leaves remainder

1 ⇒ P(2) = 1

∴ When P(x) is divided by (x – 1) (x – 2), could be given by

P(x) = {q(x)} (x – 1) (x – 2) + r(x);

where q(x) is quotiont and r(x) is remainder

(i.e. r(x) = ax + b)

⇒   P(x) = (x – 1) (x – 2) q(x) + (ax + b)

**∴   **P(1) ⇒ 0 + a + b = 2

And P(2)⇒ 0 + 2a + b = 1

on solving we get, a = – 1, b = 3

 reminder = – x + 3