**Solving Factorable Quadratic Equations**

A **quadratic equation** is a polynomial equation of degree two. The **standard form** is ax² + bx + c = 0.

There’s no magic to solving quadratic equations. Quadratic equations can be solved by **factoring** and also by **graphing.**

**The factoring method of solution:**

**Let’s do a quick review of factoring.**

**Factoring Method:**

- Express the equation in the form ax
^{2}+ bx + c = 0. - Factor the left hand side (if 0 is on the right).
- Set each of the two factors equal to zero.
- Solve for x to determine the roots (or zeros).

Simple quadratic equations with rational roots can be solved by factoring.

If you can factor, you will be able to solve factorable quadratic equations.

**Examples of Solving Quadratic Equations by Factoring:**

**Example 1: **

**Factoring with GCF**

**(greatest common factor):**

Find the largest value which can be factored from each term on the left side of the quadratic equation.

The roots (zeros) correspond to the locations of the x-intercepts of the function y = 4x^{2} – 28x.

**Example 2: Factoring Trinomial with Leading Coefficient of One: **When the leading coefficient is one, the product of the roots will be the constant term, and the sum of the roots will be the coefficient of the middle x-term.

**Example 3: Factoring Difference of Two Squares: **Remember the pattern for the difference of two squares, where the factors are identical except for the sign between the terms.

**Example 4: Factoring Trinomial with Leading Coefficient Not One: **Life gets more difficult when the leading coefficient is not one.

**Example 5: Where’s the x ^{2} ? **Sometimes you have to “work” on the equation to get the needed quadratic form. In this case, distribute, and the x

^{2}will appear.

**Example 6: Dealing with Proportions: **x

^{2}may appear when cross multiplying (“product of the means equals product of the extremes”) is employed in a proportion.