Question 169053: I need to know how to do this and the book is confusing me
Factor completely:
2x3 – 26x2 + 80x
I would appreciate any help on this.
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
 Start with the given expression
 Factor out the GCF 
Now let's focus on the inner expression 
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Looking at the expression , we can see that the first coefficient is  , the second coefficient is  , and the last term is  .
Now multiply the first coefficient by the last term to get  .
Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,2,4,5,8,10,20,40
-1,-2,-4,-5,-8,-10,-20,-40
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*40
2*20
4*10
5*8
(-1)*(-40)
(-2)*(-20)
(-4)*(-10)
(-5)*(-8)
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| First Number | Second Number | Sum | | 1 | 40 | 1+40=41 | | 2 | 20 | 2+20=22 | | 4 | 10 | 4+10=14 | | 5 | 8 | 5+8=13 | | -1 | -40 | -1+(-40)=-41 | | -2 | -20 | -2+(-20)=-22 | | -4 | -10 | -4+(-10)=-14 | | -5 | -8 | -5+(-8)=-13 |
From the table, we can see that the two numbers  and  add to (the middle coefficient).
So the two numbers and both multiply to and add to
Now replace the middle term  with  . Remember, and add to . So this shows us that  .
 Replace the second term with .
 Group the terms into two pairs.
 Factor out the GCF  from the first group.
 Factor out  from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.
 Combine like terms. Or factor out the common term 
So factors to .
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So our expression goes from and factors further to 
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Answer:
So completely factors to
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! 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.
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