SOLUTION: How do you factor: 4x squared - 17x + 4 ? This factoring thing doesn't make sense to me at all.... :(

Question 417524: How do you factor: 4x squared - 17x + 4 ?
This factoring thing doesn't make sense to me at all.... :(
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 4 and 4 respectively.

Now multiply the first coefficient 4 and the last coefficient 4 to get 16. Now what two numbers multiply to 16 and add to the middle coefficient -17? Let's list all of the factors of 16:

Factors of 16:
1,2,4,8

-1,-2,-4,-8 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 16
1*16
2*8
4*4
(-1)*(-16)
(-2)*(-8)
(-4)*(-4)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -17? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -17

First Number	Second Number	Sum
1	16	1+16=17
2	8	2+8=10
4	4	4+4=8
-1	-16	-1+(-16)=-17
-2	-8	-2+(-8)=-10
-4	-4	-4+(-4)=-8

From this list we can see that -1 and -16 add up to -17 and multiply to 16

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

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

Answer:
So factors to

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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