In order to factor , first we need to ask ourselves: What two numbers multiply to 4 and add to -5? Lets find out by listing all of the possible factors of 4
Factors:
1,2,4,
-1,-2,-4,List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to 4.
1*4=4
2*2=4
(-1)*(-4)=4
(-2)*(-2)=4
note: remember two negative numbers multiplied together make a positive number
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 | | | 4 | || | 1+4=5 | | 2 | | | 2 | || | 2+2=4 | | -1 | | | -4 | || | -1+(-4)=-5 | | -2 | | | -2 | || | -2+(-2)=-4 | We can see from the table that -1 and -4 add to -5.So the two numbers that multiply to 4 and add to -5 are: -1 and -4
Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:
substitute a=-1 and b=-4
So the equation becomes:
(x-1)(x-4)
Notice that if we foil (x-1)(x-4) we get the quadratic again
Now lets factor
Factor out This is the simplified form
Now lets factor (we're going to use x instead of b)
| 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 4 and add to 1? Lets find out by listing all of the possible factors of 4
Factors:
1,2,4,
-1,-2,-4,List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to 4.
1*4=4
2*2=4
(-1)*(-4)=4
(-2)*(-2)=4
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1
|
|