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
|
|
|
