Factoring algebraic expressions
Factoring algebraic expressions require a solid understanding of how to get the
greatest common factor(GCF)
I will not repeat the the whole process here. Therefore, go
here and review how to get the
GCF before you start studying this lesson
Basically, when factoring algebraic expressions, you will first look for the GCF and use your GCF to make your polynomial look like a multiplication problem:
GCF times( ) or
GCF times( Blank )
where blank is a polynomial with the same amount of term as the original polynomial
Recall that terms are separated by addition signs, never by multiplication sign
Example #1:
Factor x
^{2}y
^{4} + 2x
^{2}
This expression has two terms. The first term is x
^{2}y
^{4} and the second is 2x
^{2}
What you do in bold is the GCF:
x^{2} x^{2}y
^{4} + 2
x^{2}
So, we are going to make x
^{2}y
^{4} + 2x
^{2} look like:
x^{2} times ( )
Now you need to fill in the blank as shown below:
So, your first term is whatever you multiply
x^{2} to get x
^{2}y
^{4}
And whatever you multiply
x^{2} to get 2x
^{2} is your second term
Therefore, x
^{2}y
^{4} + 2x
^{2} = x
^{2}(y
^{4} + 2)
There is an easier way to solve the problem
x^{2}y
^{4} + 2
x^{2}
Still do
x^{2} times ( )
Then, in the expression
x^{2}y
^{4} + 2
x^{2}, take a pencil and cross out or erase the GCF
x^{2}.Then, whatever is left is your first and second term
Another example
2)
8Y
^{3}B
^{2} + 16Y
^{2}B
Rewrite the expression as: 8 × Y
^{2} × Y × B × B + 8 × 2Y
^{2}B
Everything in bold is the GCF
8 ×
Y^{2} × Y × B ×
B +
8 × 2
Y^{2}B
The GCF is
8Y^{2}B. The answer looks like
8Y^{2}B × ( )
In the expression
8 ×
Y^{2} × Y × B ×
B +
8 × 2
Y^{2}B, erase the GCF. Whatever is left is your first and second term
The answer is
8 ×
Y^{2} × Y × B ×
B +
8 × 2
Y^{2}B =
8Y^{2}B × (YB + 2)
3)
If instead you were factoring 8Y
^{3}B
^{2} − 16Y
^{2}B, you will do the same thing with the exception
that there will be a minus sign between the two terms. That is all!
8Y
^{3}B
^{2} − 16Y
^{2}B = 8Y
^{2}B × (YB − 2)
4)
Factor 5(x-2) + 6x(x-2)
Everything in bold is your GCF 5
(x-2) + 6x
(x-2)
So,
(x-2) × ( 5 + 6x)