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 #4 : Simplifying Quadratics

Which of the following expressions is equivalent to the product?

Explanation:

Use the difference of squares pattern

with  and  :

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 #6 : 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 #7 : 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 #1 : 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