# SOLUTION: 25x2-22xy+36y2 Factoring Trinomial Three terms

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Question 145384This question is from textbook College Algebra: Concepts and Models, Fifth Edition
: 25x2-22xy+36y2 Factoring Trinomial Three terms This question is from textbook College Algebra: Concepts and Models, Fifth Edition

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Looking at we can see that the first term is and the last term is where the coefficients are 25 and 36 respectively.

Now multiply the first coefficient 25 and the last coefficient 36 to get 900. Now what two numbers multiply to 900 and add to the middle coefficient -22? Let's list all of the factors of 900:

Factors of 900:
1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450

-1,-2,-3,-4,-5,-6,-9,-10,-12,-15,-18,-20,-25,-30,-36,-45,-50,-60,-75,-90,-100,-150,-180,-225,-300,-450 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 900
1*900
2*450
3*300
4*225
5*180
6*150
9*100
10*90
12*75
15*60
18*50
20*45
25*36
30*30
(-1)*(-900)
(-2)*(-450)
(-3)*(-300)
(-4)*(-225)
(-5)*(-180)
(-6)*(-150)
(-9)*(-100)
(-10)*(-90)
(-12)*(-75)
(-15)*(-60)
(-18)*(-50)
(-20)*(-45)
(-25)*(-36)
(-30)*(-30)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -22? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -22

First NumberSecond NumberSum
19001+900=901
24502+450=452
33003+300=303
42254+225=229
51805+180=185
61506+150=156
91009+100=109
109010+90=100
127512+75=87
156015+60=75
185018+50=68
204520+45=65
253625+36=61
303030+30=60
-1-900-1+(-900)=-901
-2-450-2+(-450)=-452
-3-300-3+(-300)=-303
-4-225-4+(-225)=-229
-5-180-5+(-180)=-185
-6-150-6+(-150)=-156
-9-100-9+(-100)=-109
-10-90-10+(-90)=-100
-12-75-12+(-75)=-87
-15-60-15+(-60)=-75
-18-50-18+(-50)=-68
-20-45-20+(-45)=-65
-25-36-25+(-36)=-61
-30-30-30+(-30)=-60

None of these pairs of factors add to -22. So the expression cannot be factored

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