SOLUTION: What is the factorization of 20xsquared+27x-8
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Question 336721: What is the factorization of 20xsquared+27x-8
Found 2 solutions by Fombitz, jim_thompson5910:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
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 20 and -8 respectively.
Now multiply the first coefficient 20 and the last coefficient -8 to get -160. Now what two numbers multiply to -160 and add to the middle coefficient 27? 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 27? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 27
| 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 -5 and 32 add up to 27 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 )
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Answer:
So factors to
If you need more help, email me at jim_thompson5910@hotmail.com
Also, feel free to check out my website.
Jim
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