Expert: Richard J. Raridon - 10/20/2004

Question
synthetic division-can you show me step by step?

3x^3-2^2+2x-5
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   x-2

Express in form of f(x)= (x-k)q(x)+r

Answer
I presume you mean 3x^3 -2x^2 +2x -5.  
if you divide by x-2, the first term in the answer is 3x^2.
So you multiply it by each term to get 3x^3-6x^2.
Subtract that from the original and you get 4x^2+2x-5.
Now your second term in your answer is 4x.
Multiply that by x-2 to get 4x^2-8x.
Subtract that from 4x^2+2x-5 to get 10x-5
That makes your final term 10 so you're subtracting 10x-20
and your total answer is f(x)=(x-2)(3x^2+4x+10) +15