SOLUTION: Factor by using trial factors. 3p^2 + 20p - 32

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Question 778412: Factor by using trial factors.
3p^2 + 20p - 32
Found 2 solutions by jim_thompson5910, psbhowmick:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression 3p%5E2%2B20p-32, we can see that the first coefficient is 3, the second coefficient is 20, and the last term is -32.


Now multiply the first coefficient 3 by the last term -32 to get %283%29%28-32%29=-96.


Now the question is: what two whole numbers multiply to -96 (the previous product) and add to the second coefficient 20?


To find these two numbers, we need to list all of the factors of -96 (the previous product).


Factors of -96:
1,2,3,4,6,8,12,16,24,32,48,96
-1,-2,-3,-4,-6,-8,-12,-16,-24,-32,-48,-96


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to -96.
1*(-96) = -96
2*(-48) = -96
3*(-32) = -96
4*(-24) = -96
6*(-16) = -96
8*(-12) = -96
(-1)*(96) = -96
(-2)*(48) = -96
(-3)*(32) = -96
(-4)*(24) = -96
(-6)*(16) = -96
(-8)*(12) = -96

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 20:


First NumberSecond NumberSum
1-961+(-96)=-95
2-482+(-48)=-46
3-323+(-32)=-29
4-244+(-24)=-20
6-166+(-16)=-10
8-128+(-12)=-4
-196-1+96=95
-248-2+48=46
-332-3+32=29
-424-4+24=20
-616-6+16=10
-812-8+12=4



From the table, we can see that the two numbers -4 and 24 add to 20 (the middle coefficient).


So the two numbers -4 and 24 both multiply to -96 and add to 20


Now replace the middle term 20p with -4p%2B24p. Remember, -4 and 24 add to 20. So this shows us that -4p%2B24p=20p.


3p%5E2%2Bhighlight%28-4p%2B24p%29-32 Replace the second term 20p with -4p%2B24p.


%283p%5E2-4p%29%2B%2824p-32%29 Group the terms into two pairs.


p%283p-4%29%2B%2824p-32%29 Factor out the GCF p from the first group.


p%283p-4%29%2B8%283p-4%29 Factor out 8 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%28p%2B8%29%283p-4%29 Combine like terms. Or factor out the common term 3p-4


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Answer:


So 3p%5E2%2B20p-32 factors to %28p%2B8%29%283p-4%29.


In other words, 3p%5E2%2B20p-32=%28p%2B8%29%283p-4%29.


Note: you can check the answer by expanding %28p%2B8%29%283p-4%29 to get 3p%5E2%2B20p-32 or by graphing the original expression and the answer (the two graphs should be identical).

Answer by psbhowmick(878) About Me  (Show Source):