SOLUTION: What is the factored form of 4x^2+13-12?
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Question 112297: What is the factored form of 4x^2+13-12?
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 -12 respectively.
Now multiply the first coefficient 4 and the last coefficient -12 to get -48. Now what two numbers multiply to -48 and add to the middle coefficient 13? Let's list all of the factors of -48:
Factors of -48:
1,2,3,4,6,8,12,16,24,48
-1,-2,-3,-4,-6,-8,-12,-16,-24,-48 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -48
(1)*(-48)
(2)*(-24)
(3)*(-16)
(4)*(-12)
(6)*(-8)
(-1)*(48)
(-2)*(24)
(-3)*(16)
(-4)*(12)
(-6)*(8)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 13? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 13
| First Number | Second Number | Sum | | 1 | -48 | 1+(-48)=-47 |
| 2 | -24 | 2+(-24)=-22 |
| 3 | -16 | 3+(-16)=-13 |
| 4 | -12 | 4+(-12)=-8 |
| 6 | -8 | 6+(-8)=-2 |
| -1 | 48 | -1+48=47 |
| -2 | 24 | -2+24=22 |
| -3 | 16 | -3+16=13 |
| -4 | 12 | -4+12=8 |
| -6 | 8 | -6+8=2 |
From this list we can see that -3 and 16 add up to 13 and multiply to -48
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 )
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