In order to factor , first we need to ask ourselves: What two numbers multiply to -14 and add to 5? Lets find out by listing all of the possible factors of -14
Factors:
1,2,7,14,
-1,-2,-7,-14,List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to -14.
(-1)*(14)=-14
(-2)*(7)=-14
Now which of these pairs add to 5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 5
| First Number | | | Second Number | | | Sum | | 1 | | | -14 | || | 1+(-14)=-13 | | 2 | | | -7 | || | 2+(-7)=-5 | | -1 | | | 14 | || | (-1)+14=13 | | -2 | | | 7 | || | (-2)+7=5 | We can see from the table that -2 and 7 add to 5.So the two numbers that multiply to -14 and add to 5 are: -2 and 7
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=7
So the equation becomes:
(x-2)(x+7)
Notice that if we foil (x-2)(x+7) we get the quadratic again
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 21 and add to 10? Lets find out by listing all of the possible factors of 21
Factors:
1,3,7,21,
-1,-3,-7,-21,List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to 21.
1*21=21
3*7=21
(-1)*(-21)=21
(-3)*(-7)=21
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 10? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 10
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