1. a) Write down the highest possible degree of he remainder when a
polynomial P(x) is divided b (x-1)(x+2).
ANS: 1
b) It is given that when P(x ) in a is divided by x-1 and x+2, the
remainders are -4 and -28 respectively. Find the remainder when P(x)
is divided by(x-1)(x+2).
ANS: 8x-12
How can i get the answer? Thanks!!
Maths Question
2010-01-26 4:49 am
回答 (2)
2010-01-26 5:01 am
✔ 最佳答案
(1) The highest degree of the remainder is less than the degree of the given divisor. Since the given divisor is of degree 2, the highest possible degree of the remainder is 1.(2) Let P(x) = Q(x)(x – 1)(x + 2) + (ax + b) where Q(x) is the quotient and ax + b is the remainder. By remainder theorem, remainder when P(x) is divided by (x – 1) is P(1) = Q(1)(1 – 1)(1 + 2) + a + b = -4
Or a + b = -4 … (1)
Remainder when P(x) is divided by (x + 2) is P(-2) = Q(-2)(-2 – 1)(-2 + 2) – 2a + b = -28
Or -2a + b = -28 …(2)
(1) – (2) => 3a = 24
a = 8
Sub into (1), 8 + b = -4 => b = -12
Hence the remainder is 8x – 12
2010-01-26 4:52 am
OK! I think your questions are quite good!
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