Polynomial (1 Viewer)

[conman]

Whe P(x) is divided by (x-2) and (x-3) the remainders are 4 and 9 respectively. What is the remainder when P(x) is divided by (x-2)(x-3)

 

[pLuvia]

Let the remainder be ax+b, where a and b are constants
When x=2
2a+b=4
When x=3
3a+b=9

Find a and b
a=5
b=-6

Therefore the remainder is 5x-6, so when P(x) is divided by (x-2)(x-3), the remainder is 5x-6

 

[conman]

Thanks a lot

 

[bos1234]

He took the remainder as ax+b because if A(x) is x^2 then the power of the remainder must be less that 2

Similarly if A(x) has a power of 5
R(x) must have a remainder of less than 5