# Factorization!!

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
5 years, 1 month ago

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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

- 5 years, 1 month ago