Factoring Polynomials(plus 4 examples)
Factoring polynomials is a piece of cake once you understand how to do it.
Let’s go through an example first:
2
x −15 x+54
1) You start out by putting the “x” into two different brackets, like so:
**Note you do this because, x is being squared**
(x)( x)
2) You look at the signs of the polynomial:
The first sign tells you what sign the “bigger bracket” will have.
The second sign tells you whether the signs will be the same or different
Let’s first look at the first sign which is a negative(-), this means that the bigger bracket will contain a
negative. Now we look at the second bracket to see whether the signs will be the same or different.
If the sign is a plus(+) then they will be the same, otherwise if it's a minus(-) they will be different. So
in our case it would have the same sign. This means that we would have a negative(-) in one bracket
and a negative(-) in the other bracket. So the brackets would look like this now:
¿
3) You need to find out what goes in each bracket:
You do this by finding the factors of 54 that give you -15 which is the coefficient of x.
54 has many factors, but it is your job to find the factors that give you -15. In this case the factors
would be 6 and 9. This gives you 15. You might say that's not -15 though, and you would be right.
But how it is made into -15 is through the signs of the brackets, so from the two negatives in the
brackets. You can see this if you multiply the brackets out once you’ve solved it. But let’s first
complete the brackets.
You would now insert the 6 and 9 into the brackets so it would look like this:
(x−9)(x−6)
In this case it doesn’t matter which number you put in which bracket, but in other sums it will matter.
Let’s see now how we would get -15 from this. It will look like this if you use FOIL and
multiply it out:
Factoring polynomials is a piece of cake once you understand how to do it.
Let’s go through an example first:
2
x −15 x+54
1) You start out by putting the “x” into two different brackets, like so:
**Note you do this because, x is being squared**
(x)( x)
2) You look at the signs of the polynomial:
The first sign tells you what sign the “bigger bracket” will have.
The second sign tells you whether the signs will be the same or different
Let’s first look at the first sign which is a negative(-), this means that the bigger bracket will contain a
negative. Now we look at the second bracket to see whether the signs will be the same or different.
If the sign is a plus(+) then they will be the same, otherwise if it's a minus(-) they will be different. So
in our case it would have the same sign. This means that we would have a negative(-) in one bracket
and a negative(-) in the other bracket. So the brackets would look like this now:
¿
3) You need to find out what goes in each bracket:
You do this by finding the factors of 54 that give you -15 which is the coefficient of x.
54 has many factors, but it is your job to find the factors that give you -15. In this case the factors
would be 6 and 9. This gives you 15. You might say that's not -15 though, and you would be right.
But how it is made into -15 is through the signs of the brackets, so from the two negatives in the
brackets. You can see this if you multiply the brackets out once you’ve solved it. But let’s first
complete the brackets.
You would now insert the 6 and 9 into the brackets so it would look like this:
(x−9)(x−6)
In this case it doesn’t matter which number you put in which bracket, but in other sums it will matter.
Let’s see now how we would get -15 from this. It will look like this if you use FOIL and
multiply it out:
