Question 115752: Factor these ?
4x^2 -12x -40
2x^2 -16x +30
Found 2 solutions by Gator Tutoring, jim_thompson5910:
Answer by Gator Tutoring(5)   (Show Source):
You can put this solution on YOUR website! 1.Factor, 2x^2 -16x +30
set up parenthesis
( + ) * ( + )
what 2 numbers multiply to give you 2x^2?
place those numbers here:
( NUM + ) * ( NUM + )
( 2x + ) * ( x + )
what 2 numbers multiply to give you 30?
place those numbers here:
( + NUM ) * ( + NUM )
( 2x - 10 ) * ( x - 3 )
note that I changed the signs from positive to negative.
Answer:
( 2x - 10 ) * ( x - 3 )
to check if answer is correct:
If you multiply this out you will get
2x^2 -16x +30
note:
Understand that this method requires you to pick
a couple of numbers and see if they work. If they do not work then pick another two. also note that the signs (+/-) also may need to be changed.
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Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! #1
Looking at  we can see that the first term is  and the last term is  where the coefficients are 4 and -40 respectively.
Now multiply the first coefficient 4 and the last coefficient -40 to get -160. Now what two numbers multiply to -160 and add to the middle coefficient -12? Let's list all of the factors of -160:
Factors of -160:
1,2,4,5,8,10,16,20,32,40,80,160
-1,-2,-4,-5,-8,-10,-16,-20,-32,-40,-80,-160 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -160
(1)*(-160)
(2)*(-80)
(4)*(-40)
(5)*(-32)
(8)*(-20)
(10)*(-16)
(-1)*(160)
(-2)*(80)
(-4)*(40)
(-5)*(32)
(-8)*(20)
(-10)*(16)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to -12? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -12
| First Number | Second Number | Sum | | 1 | -160 | 1+(-160)=-159 | | 2 | -80 | 2+(-80)=-78 | | 4 | -40 | 4+(-40)=-36 | | 5 | -32 | 5+(-32)=-27 | | 8 | -20 | 8+(-20)=-12 | | 10 | -16 | 10+(-16)=-6 | | -1 | 160 | -1+160=159 | | -2 | 80 | -2+80=78 | | -4 | 40 | -4+40=36 | | -5 | 32 | -5+32=27 | | -8 | 20 | -8+20=12 | | -10 | 16 | -10+16=6 |
From this list we can see that 8 and -20 add up to -12 and multiply to -160
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
#2
Looking at  we can see that the first term is  and the last term is  where the coefficients are 2 and 30 respectively.
Now multiply the first coefficient 2 and the last coefficient 30 to get 60. Now what two numbers multiply to 60 and add to the middle coefficient -16? Let's list all of the factors of 60:
Factors of 60:
1,2,3,4,5,6,10,12,15,20,30,60
-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 60
1*60
2*30
3*20
4*15
5*12
6*10
(-1)*(-60)
(-2)*(-30)
(-3)*(-20)
(-4)*(-15)
(-5)*(-12)
(-6)*(-10)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -16? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -16
| First Number | Second Number | Sum | | 1 | 60 | 1+60=61 | | 2 | 30 | 2+30=32 | | 3 | 20 | 3+20=23 | | 4 | 15 | 4+15=19 | | 5 | 12 | 5+12=17 | | 6 | 10 | 6+10=16 | | -1 | -60 | -1+(-60)=-61 | | -2 | -30 | -2+(-30)=-32 | | -3 | -20 | -3+(-20)=-23 | | -4 | -15 | -4+(-15)=-19 | | -5 | -12 | -5+(-12)=-17 | | -6 | -10 | -6+(-10)=-16 |
From this list we can see that -6 and -10 add up to -16 and multiply to 60
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
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