SOLUTION: Show that (x-2) is a factor of f(x) = x³-2x²-4x+8. Hence factorise f(x) completely.

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Question 1132054: Show that (x-2) is a factor of f(x) = x³-2x²-4x+8.
Hence factorise f(x) completely.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): 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)

Answer by ikleyn(52946)   (Show Source): You can put this solution on YOUR website!
.
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.

Solved.

--------------------------

See the lessons
    - Divisibility of polynomial f(x) by binomial x-a and the Remainder theorem
    - Solved problems on the Remainder thoerem
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"Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem".

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