Question

Consider the
polynomial
P(x)=3x^4-ax^3+2ax^2-x-b
If the remainder
when P(x) is
divided by x+1
is 6 and 1 is a
zero of P(x) ,
find a and
b?​

Answer 1

Using basics of remainder theorem, remainder of f(x) when divided with (x-a) will be f(a).

So from the above data, f(-1) = 6 and f(1) = 0.

Substituting it, 3(-1)^4-a(-1)^3+2a(-1)^2-(-1)-b = 6

i.e. 3+a+2a+1-b = 6 => 3a - b = 2

Also 3(1)^4-a(1)^3+2a(1)^2-(1)-b = 0

i.e. 3-a+2a-1-b = 0 => a - b = -2

Solving these two equations, we can get a = 2, b = 4.