SOLUTION: Okay so I am having a brain-freeze on how to factor more challenging polynomials, how do you factor: 40k^2-112k+24

Question 481981: Okay so I am having a brain-freeze on how to factor more challenging polynomials, how do you factor:
40k^2-112k+24
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 try to factor 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 :
1,3,5,15
-1,-3,-5,-15

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*15 = 15
3*5 = 15
(-1)*(-15) = 15
(-3)*(-5) = 15

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	15	1+15=16
3	5	3+5=8
-1	-15	-1+(-15)=-16
-3	-5	-3+(-5)=-8

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

===============================================================

Answer:

So simply factors to

In other words, .

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