What is the remainder when the polynomial p(x) = x200 – 2x199 + x50

1.	What is the remainder when the polynomial p(x) = x200 – 2x199 + x50 – 2x49 + x2 + x + 1 is divided by (x – 1) (x – 2) ? (1) 1 (2) 7 (3) 2x + 1 (4) 6x – 5
Answer» Correct option (4) 6x – 5 Explanation: f(x) = x²⁰⁰ – 2x¹⁹⁹ + x⁵⁰–2x⁴⁹+ x²+ x + 1 f(x) = (x – 1)(x – 2) q(x) + ax + b 1 – 2 + 1 – 2 + 1 + 1 + 1 = a + b 1 = a + b 2²⁰⁰ – 2²⁰⁰ + 2⁵ – 2⁵⁰+ 4 + 2 + 1 = 2a + b 7 = 2a + b – 6 = – a ⇒ a = 6 ∴ b = –5 ∴ 6b = –5

What is the remainder when the polynomial p(x) = x200 – 2x199 + x50 – 2x49 + x2 + x + 1 is divided by (x – 1) (x – 2) ? (1) 1 (2) 7 (3) 2x + 1 (4) 6x – 5

Answer»

Correct option (4) 6x – 5

Explanation:

f(x) = x²⁰⁰ – 2x¹⁹⁹ + x⁵⁰–2x⁴⁹+ x²+ x + 1

f(x) = (x – 1)(x – 2) q(x) + ax + b

1 – 2 + 1 – 2 + 1 + 1 + 1 = a + b

1 = a + b

2²⁰⁰ – 2²⁰⁰ + 2⁵ – 2⁵⁰+ 4 + 2 + 1 = 2a + b

7 = 2a + b

– 6 = – a ⇒ a = 6

∴ b = –5

∴ 6b = –5

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What is the remainder when the polynomial p(x) = x200 – 2x199 + x50 – 2x49 + x2 + x + 1 is divided by (x – 1) (x – 2) ? (1) 1 (2) 7 (3) 2x + 1 (4) 6x – 5

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