When [equation] is divided by (x-1) the remainder is 7. When it is divided by (x+1) the remainder is 3. Determine the values of a &b .
Can somebody please just explain the method... thanks:)

Question

When [equation] is divided by (x-1) the remainder is 7. When it is divided by (x+1) the remainder is 3. Determine the values of a &b .
Can somebody please just explain the method... thanks:)

anonymous · Answer

$$\huge x^4-4x^3+ax^2+bx+1 $$

anonymous · Answer

Have you tried synthetic division?

anonymous · Answer

but there are 3 variables .. :S

anonymous · Answer

Yeah but you know a lot of algebra to deal with them.

anonymous · Answer

Hmmm, I'm not exactly sure what the trick for this is.

anonymous · Answer

$$
\large
x^4-4x^3+ax^2+bx+1=(x-1)(cx^3+dx^2+ex+f)+7
$$

anonymous · Answer

@ burhan101 
use factor and remainder theorem

anonymous · Answer

when f(x) is divided by (x-a)  the remainder is given by f(a)

anonymous · Answer

thus here f(x) =x^4−4x^3+ax^2+bx+1
f(1)=7 and f(-1)=3

u will get two equation in two unknowns and u can solev them to know a and b

anonymous · Answer

thus
 a+b=9
and a-b -3

thus solving above two eq 
we have a=3 and b=6