When f(x) is divided by ( x-3 ) and ( 2x+1 ), the remainders are 6 and -1 respectively. Find the remainder when f(x) is divided by ( 2x^2-5x-3 ).

Question

kayc · Answer

Is the answer possibly 2x + 0 ...?

raden · Answer

first, 2x^2-5x-3 =(2x+1)(x-3), and suppose ax+b is remainders of f(x) when divided by 2x^2-5x-3. 
f(x) is divided by ( x-3 ) and its remainders is 6, it means f(3)=6 or
3a+b=3. ...(1)
f(x) is divided by (2x+1 ) and its remainders is -1, it means f(-1/2)=-1 or
-1/2*a+b=-1.  ...(2) 
from (1) and (2), using elimination and subtitution method for solve a and b.

raden · Answer

yea, i got a=2, and b=0
so, its remainder is 2x+0=2x

kayc · Answer

Okay, thanks !

raden · Answer

welcome