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When a polynomial f(x) is divided by (x-1),the remainder is 5 and when it is divided by (x-2), the remainder is 7. Find the remainder when it is divided by (x-1)(x-2).

Note by Parmeet Singh 4 years, 8 months ago

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2 \times 3

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there is a polynomial of degree 2 i.e. a quadratic polynomial

using division algorithm f(x)= D(x).Q(x) + R(x)

put x-1 =0 x=1

x-2=0 x=2

f(x)=(x-1)(x-2) .Q(x) +R(x) Let R(x) be Ax+B

now using factor theorem,

f(1)=(0)(-1) + (A+B) = 5 f(2)=(1)(0)+ (2A+B) =7 A+B=5 {1}

2A+B=7 {2}

Sub {1} from {2}

2A+B -A-B =7-5 A=2 B=3

Hence, the remainder is 2x+3

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`\sin \theta`

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TopNewestthere is a polynomial of degree 2 i.e. a quadratic polynomial

using division algorithm

f(x)= D(x).Q(x) + R(x)

put x-1 =0

x=1

x-2=0

x=2

f(x)=(x-1)(x-2) .Q(x) +R(x)

Let R(x) be Ax+B

now using factor theorem,

f(1)=(0)(-1) + (A+B) = 5

f(2)=(1)(0)+ (2A+B) =7

A+B=5 {1}

2A+B=7 {2}

Sub {1} from {2}

2A+B -A-B =7-5

A=2

B=3

Hence, the remainder is 2x+3

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