You can put this solution on YOUR website! Can use synthetic division with 2
2/1--- -2---- -4-----8
1 0 -4 0
that is x^2-4
so the factors are (x-2)(x^2-4) or (x-2)(x-2)(x+2), or (x-2)^2*(x+2)
This problem is to use the "Remainder theorem".
The Remainder theorem says that the binomial (x-a) is a factor of a polynomial
f(x) =
if and only if the value of "a" is the root of the polynomial f(x), i.e. f(a) = 0.
So, in your case, to show that (x-2) is a factor of the given polynomial
f(x) = ,
you need simply calculate
f(5) = = 8 - 8 - 8 + 8 = 0
and make sure that it is equal to zero.
