You can put this solution on YOUR website! In order to factor , first multiply 5 and -6 to get -30 and we need to ask ourselves: What two numbers multiply to -30 and add to 7? Lets find out by listing all of the possible factors of -30
Factors:
1,2,3,5,6,10,15,30,
-1,-2,-3,-5,-6,-10,-15,-30, List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to -30.
(-1)*(30)=-30
(-2)*(15)=-30
(-3)*(10)=-30
(-5)*(6)=-30
Now which of these pairs add to 7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 7
First Number
|
Second Number
|
Sum
1
|
-30
|
|
1+(-30)=-29
2
|
-15
|
|
2+(-15)=-13
3
|
-10
|
|
3+(-10)=-7
5
|
-6
|
|
5+(-6)=-1
-1
|
30
|
|
(-1)+30=29
-2
|
15
|
|
(-2)+15=13
-3
|
10
|
|
(-3)+10=7
-5
|
6
|
|
(-5)+6=1
We can see from the table that -3 and 10 add to 7. So the two numbers that multiply to -30 and add to 7 are: -3 and 10
So the original quadratic
breaks down to this (just replace with the two numbers that multiply to -30 and add to 7, which are: -3 and 10)
Group the first two terms together and the last two terms together like this:
Factor a y out of the first group and factor a 2 out of the second group.
Now since we have a common term we can combine the two terms.
Combine like terms.
Answer:
So the quadratic factors to
Notice how foils back to our original problem . This verifies our answer.
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