SOLUTION: Factor the following trinomial completely. x^2 – 11x - 60

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Question 77420: Factor the following trinomial completely.
x^2 – 11x - 60
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor , first we need to ask ourselves: What two numbers multiply to -60 and add to -11? Lets find out by listing all of the possible factors of -60


Factors:

1,2,3,4,5,6,10,12,15,20,30,60,

-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -60.

(-1)*(60)=-60

(-2)*(30)=-60

(-3)*(20)=-60

(-4)*(15)=-60

(-5)*(12)=-60

(-6)*(10)=-60

Now which of these pairs add to -11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -11

||||||||||||
First Number|Second Number|Sum
1|-60|1+(-60)=-59
2|-30|2+(-30)=-28
3|-20|3+(-20)=-17
4|-15|4+(-15)=-11
5|-12|5+(-12)=-7
6|-10|6+(-10)=-4
-1|60|(-1)+60=59
-2|30|(-2)+30=28
-3|20|(-3)+20=17
-4|15|(-4)+15=11
-5|12|(-5)+12=7
-6|10|(-6)+10=4
We can see from the table that 4 and -15 add to -11.So the two numbers that multiply to -60 and add to -11 are: 4 and -15 Now we substitute these numbers into a and b of the general equation of a product of linear factors which is: substitute a=4 and b=-15 So the equation becomes: (x+4)(x-15) Notice that if we foil (x+4)(x-15) we get the quadratic again

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