GED Math : Simplifying Quadratics
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Example Questions
Example Question #1 : Simplifying Quadratics
This is a quadratic equation, but it is not in standard form.
We express it in standard form as follows, using the FOIL technique:
Now factor the quadratic expression on the left. It can be factored as
where 
By trial and error we find that 
can be rewritten as
Set each linear binomial equal to 0 and solve separately:
The solution set is 
Example Question #2 : Simplifying Quadratics
Subtract:
can be determined by subtracting the coefficients of like terms. We can do this vertically as follows:
By switching the symbols in the second expression we can transform this to an addition problem, and add coefficients:
Example Question #2 : Simplifying Quadratics
Add:
can be determined by adding the coefficients of like terms. We can do this vertically as follows:
Example Question #3 : Simplifying Quadratics
Which of the following expressions is equivalent to the product?
Use the difference of squares pattern
with 
Example Question #4 : Simplifying Quadratics
Which of the following expressions is equivalent to the product?
Use the difference of squares pattern
with 
Example Question #6 : Simplifying Quadratics
Simplify:
Start by factoring the numerator. Notice that each term in the numerator has an 
Next, factor the terms in the parentheses. You will want two numbers that multiply to 
Next, factor the denominator. For the denominator, we will want two numbers that multiply to 
Now that both the denominator and numerator have been factored, rewrite the fraction in its factored form.
Cancel out any terms that appear in both the numerator and denominator.
Example Question #6 : Simplifying Quadratics
Simplify the following expression:
Start by factoring the numerator.
To factor the numerator, you will need to find 
Next, factor the denominator.
To factor the denominator, you will need to find two numbers that add up to 
Rewrite the fraction in its factored form.
Since 
Example Question #5 : Simplifying Quadratics
Simplify:
We need to factor both the numerator and the denominator to determine what can cancel each other out.
If we factor the numerator:
Two numbers which add to 6 and multiply to give you -7.
Those numbers are 7 and -1.
If we factor the denominator:
First factor out a 2 
Two numbers which add to -4 and multiply to give you 3
Those numbers are -3 and -1
Now we can re-write our expression with a product of factors:
We can divide 
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