SOLUTION: how do you simplify 15x^2+75x-1260

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Question 347687: how do you simplify 15x^2+75x-1260
Found 2 solutions by jim_thompson5910, Fombitz:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

15x%5E2%2B75x-1260 Start with the given expression


15%28x%5E2%2B5x-84%29 Factor out the GCF 15


Now let's focus on the inner expression x%5E2%2B5x-84




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Looking at 1x%5E2%2B5x-84 we can see that the first term is 1x%5E2 and the last term is -84 where the coefficients are 1 and -84 respectively.

Now multiply the first coefficient 1 and the last coefficient -84 to get -84. Now what two numbers multiply to -84 and add to the middle coefficient 5? Let's list all of the factors of -84:



Factors of -84:
1,2,3,4,6,7,12,14,21,28,42,84

-1,-2,-3,-4,-6,-7,-12,-14,-21,-28,-42,-84 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -84
(1)*(-84)
(2)*(-42)
(3)*(-28)
(4)*(-21)
(6)*(-14)
(7)*(-12)
(-1)*(84)
(-2)*(42)
(-3)*(28)
(-4)*(21)
(-6)*(14)
(-7)*(12)

note: remember, the product of a negative and a positive number is a negative number


Now which of these pairs add to 5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 5

First NumberSecond NumberSum
1-841+(-84)=-83
2-422+(-42)=-40
3-283+(-28)=-25
4-214+(-21)=-17
6-146+(-14)=-8
7-127+(-12)=-5
-184-1+84=83
-242-2+42=40
-328-3+28=25
-421-4+21=17
-614-6+14=8
-712-7+12=5



From this list we can see that -7 and 12 add up to 5 and multiply to -84


Now looking at the expression 1x%5E2%2B5x-84, replace 5x with -7x%2B12x (notice -7x%2B12x adds up to 5x. So it is equivalent to 5x)

1x%5E2%2Bhighlight%28-7x%2B12x%29%2B-84


Now let's factor 1x%5E2-7x%2B12x-84 by grouping:


%281x%5E2-7x%29%2B%2812x-84%29 Group like terms


x%28x-7%29%2B12%28x-7%29 Factor out the GCF of x out of the first group. Factor out the GCF of 12 out of the second group


%28x%2B12%29%28x-7%29 Since we have a common term of x-7, we can combine like terms

So 1x%5E2-7x%2B12x-84 factors to %28x%2B12%29%28x-7%29


So this also means that 1x%5E2%2B5x-84 factors to %28x%2B12%29%28x-7%29 (since 1x%5E2%2B5x-84 is equivalent to 1x%5E2-7x%2B12x-84)



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So our expression goes from 15%28x%5E2%2B5x-84%29 and factors further to 15%28x%2B12%29%28x-7%29


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Answer:

So 15x%5E2%2B75x-1260 factors to 15%28x%2B12%29%28x-7%29

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

Also, feel free to check out my tutoring website

Jim

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Divide all terms by 15, since all terms are divisible by 3 and 5.