Question 169053
I need to know how to do this and the book is confusing me 
Factor completely:
2x3 – 26x2 + 80x 
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1st, notice that all the coefficients are even numbers.  That means you can divide by 2.
Then, each term has an "x", so you can divide by x.
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2x3 – 26x2 + 80x 
Divide by 2x
= 2x*(x^2 - 13x + 40)
Now you need to see if *(x^2 - 13x + 40) can be factored.
(x^2 - 13x + 40)
If it can, it will be in the form (x + a)*(x + b)
The product a*b will be 40, and the sum a+b will be -13.  Since it's a positive 40, they have to be the same sign, so it's the sum, not the difference.
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Look at all the factors of 40.
1*40
2*20
4*10
5*8
Look for a pair that will add to 13.  Only 5 and 8 do, so that's the solution.
It's (x-5)*(x-8) = x^2-13x+40.
So the answer is:
2x(x-5)(x-8)
It's not a mystery, just the use of a logical approach.