In order to factor , first we need to ask ourselves: What two numbers multiply to -9 and add to 0? Lets find out by listing all of the possible factors of -9
Factors:
1,3,9,
-1,-3,-9,List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to -9.
(-1)*(9)=-9
(-3)*(3)=-9
Now which of these pairs add to 0? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 0
| First Number | | | Second Number | | | Sum | | 1 | | | -9 | || | 1+(-9)=-8 | | 3 | | | -3 | || | 3+(-3)=0 | | -1 | | | 9 | || | (-1)+9=8 | | -3 | | | 3 | || | (-3)+3=0 | We can see from the table that -3 and 3 add to 0.So the two numbers that multiply to -9 and add to 0 are: -3 and 3
Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:
substitute a=-3 and b=3
So the equation becomes:
(x-3)(x+3)
Notice that if we foil (x-3)(x+3) we get the quadratic again
So the denominator factors to:
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Factor the numerator
| 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 10 and add to 7? Lets find out by listing all of the possible factors of 10
Factors:
1,2,5,10,
-1,-2,-5,-10,List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to 10.
1*10=10
2*5=10
(-1)*(-10)=10
(-2)*(-5)=10
note: remember two negative numbers multiplied together make a positive number
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 | | | 10 | || | 1+10=11 | | 2 | | | 5 | || | 2+5=7 | | -1 | | | -10 | || | -1+(-10)=-11 | | -2 | | | -5 | || | -2+(-5)=-7 | We can see from the table that 2 and 5 add to 7. So the two numbers that multiply to 10 and add to 7 are: 2 and 5
Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:
substitute a=2 and b=5
So the equation becomes:
(x+2)(x+5)
Notice that if we foil (x+2)(x+5) we get the quadratic again
So the numerator factors to:
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Factor the denominator
| 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 15 and add to 8? Lets find out by listing all of the possible factors of 15
Factors:
1,3,5,15,
-1,-3,-5,-15,List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to 15.
1*15=15
3*5=15
(-1)*(-15)=15
(-3)*(-5)=15
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 8
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