# GED Math : Simplifying Quadratics

## Example Questions

### Example Question #1 : Simplifying Quadratics

Explanation:

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 , so

can be rewritten as

.

Set each linear binomial equal to 0 and solve separately:

The solution set is .

### Example Question #2 : Simplifying Quadratics

Subtract:

Explanation:

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 #1 : Simplifying Quadratics

Explanation:

can be determined by adding the coefficients of like terms. We can do this vertically as follows:

### Example Question #2 : Simplifying Quadratics

Which of the following expressions is equivalent to the product?

Explanation:

Use the difference of squares pattern

with  and  :

### Example Question #3 : Simplifying Quadratics

Which of the following expressions is equivalent to the product?

Explanation:

Use the difference of squares pattern

with  and  :

### Example Question #4 : Simplifying Quadratics

Simplify:

Explanation:

Start by factoring the numerator. Notice that each term in the numerator has an , so we can write the following:

Next, factor the terms in the parentheses. You will want two numbers that multiply to  and add to .

Next, factor the denominator. For the denominator, we will want two numbers that multiply to  and add 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 #4 : Simplifying Quadratics

Simplify the following expression:

Explanation:

Start by factoring the numerator.

To factor the numerator, you will need to find  numbers that add up to  and multiply to .

Next, factor the denominator.

To factor the denominator, you will need to find two numbers that add up to  and multiply to .

Rewrite the fraction in its factored form.

Since  is found in both numerator and denominator, they will cancel out.

### Example Question #5 : Simplifying Quadratics

Simplify:

Explanation:

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  and  to give us 1, so we are left with