SOLUTION: t^2-2t-15

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Question 644696: t^2-2t-15
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor this.



Looking at the expression t%5E2-2t-15, we can see that the first coefficient is 1, the second coefficient is -2, and the last term is -15.


Now multiply the first coefficient 1 by the last term -15 to get %281%29%28-15%29=-15.


Now the question is: what two whole numbers multiply to -15 (the previous product) and add to the second coefficient -2?


To find these two numbers, we need to list all of the factors of -15 (the previous product).


Factors of -15:
1,3,5,15
-1,-3,-5,-15


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


These factors pair up and multiply to -15.
1*(-15) = -15
3*(-5) = -15
(-1)*(15) = -15
(-3)*(5) = -15

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -2:


First NumberSecond NumberSum
1-151+(-15)=-14
3-53+(-5)=-2
-115-1+15=14
-35-3+5=2



From the table, we can see that the two numbers 3 and -5 add to -2 (the middle coefficient).


So the two numbers 3 and -5 both multiply to -15 and add to -2


Now replace the middle term -2t with 3t-5t. Remember, 3 and -5 add to -2. So this shows us that 3t-5t=-2t.


t%5E2%2Bhighlight%283t-5t%29-15 Replace the second term -2t with 3t-5t.


%28t%5E2%2B3t%29%2B%28-5t-15%29 Group the terms into two pairs.


t%28t%2B3%29%2B%28-5t-15%29 Factor out the GCF t from the first group.


t%28t%2B3%29-5%28t%2B3%29 Factor out 5 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.


%28t-5%29%28t%2B3%29 Combine like terms. Or factor out the common term t%2B3


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Answer:


So t%5E2-2t-15 factors to %28t-5%29%28t%2B3%29.


In other words, t%5E2-2t-15=%28t-5%29%28t%2B3%29.


Note: you can check the answer by expanding %28t-5%29%28t%2B3%29 to get t%5E2-2t-15 or by graphing the original expression and the answer (the two graphs should be identical).

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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
t%5E2-2t-15...use quadratic formula

t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

t+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-15%29+%29%29%2F%282%2A1%29+

t+=+%282+%2B-+sqrt%28+4%2B60+%29%29%2F2+

t+=+%282+%2B-+sqrt%28+64+%29%29%2F2+

t+=+%282+%2B-+8%29%2F2+

solutions:

t+=+%282+%2B+8%29%2F2+
t+=+10%2F2+
t+=+5+
or
t+=+%282+-+8%29%2F2+
t+=+-6%2F2+
t+=+-3+
+graph%28+600%2C+600%2C+-10%2C+10%2C+-20%2C+10%2C+x%5E2-2x-15%29+