SOLUTION: how do you do this problem v(squared)-11v-60

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: how do you do this problem v(squared)-11v-60      Log On


   

Question 278208: how do you do this problem
v(squared)-11v-60
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want to factor this.



Looking at the expression v%5E2-11v-60, we can see that the first coefficient is 1, the second coefficient is -11, and the last term is -60.


Now multiply the first coefficient 1 by the last term -60 to get %281%29%28-60%29=-60.


Now the question is: what two whole numbers multiply to -60 (the previous product) and add to the second coefficient -11?


To find these two numbers, we need to list all of the factors of -60 (the previous product).


Factors of -60:
1,2,3,4,5,6,10,12,15,20,30,60
-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60


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


These factors pair up and multiply to -60.
1*(-60) = -60
2*(-30) = -60
3*(-20) = -60
4*(-15) = -60
5*(-12) = -60
6*(-10) = -60
(-1)*(60) = -60
(-2)*(30) = -60
(-3)*(20) = -60
(-4)*(15) = -60
(-5)*(12) = -60
(-6)*(10) = -60

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -11:


First NumberSecond NumberSum
1-601+(-60)=-59
2-302+(-30)=-28
3-203+(-20)=-17
4-154+(-15)=-11
5-125+(-12)=-7
6-106+(-10)=-4
-160-1+60=59
-230-2+30=28
-320-3+20=17
-415-4+15=11
-512-5+12=7
-610-6+10=4



From the table, we can see that the two numbers 4 and -15 add to -11 (the middle coefficient).


So the two numbers 4 and -15 both multiply to -60 and add to -11


Now replace the middle term -11v with 4v-15v. Remember, 4 and -15 add to -11. So this shows us that 4v-15v=-11v.


v%5E2%2Bhighlight%284v-15v%29-60 Replace the second term -11v with 4v-15v.


%28v%5E2%2B4v%29%2B%28-15v-60%29 Group the terms into two pairs.


v%28v%2B4%29%2B%28-15v-60%29 Factor out the GCF v from the first group.


v%28v%2B4%29-15%28v%2B4%29 Factor out 15 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.


%28v-15%29%28v%2B4%29 Combine like terms. Or factor out the common term v%2B4


===============================================================


Answer:


So v%5E2-11v-60 factors to %28v-15%29%28v%2B4%29.


In other words, v%5E2-11v-60=%28v-15%29%28v%2B4%29.


Note: you can check the answer by expanding %28v-15%29%28v%2B4%29 to get v%5E2-11v-60 or by graphing the original expression and the answer (the two graphs should be identical).