## Solving Quadratic Equations By Factoring

#### Aligned To Common Core Standard:

**High School** - HSA-REI.B.4b

How to Solve Quadratic Equations By Factoring -
If a polynomial is placed to equal value, i.e. an integer or another polynomial, then the result becomes an equation. However, the polynomial is written in the form of ax^{2}+bx+c=0 is known as the quadratic equations. There are two ways that we can solve this equation and find its roots. The first way is to solve it by using the quadratic formula. The second way is to use factorization for solving the quadratic equation.
For instance, we have an equation x^{2} - 7x + 12 = 0
Factorize the equation, by separately writing 7x, i.e., in the form -3x - 4x. The factors are made because 3 multiplied by 4 is 12; which is the last term in the equation.
x^{2} - 3x - 4x + 12 = 0
Now, we group pairs, taking commons
x(x-3) - 4(x-3) = 0
In the first two terms, the only thing common is x. While, in the last two terms, 4 is common because 12 is the multiple of 4.
Now, we factor out to (x – 3) and write it in the form of: (x-3) (x-4)=0
Let us now write each of these factors individually and equal them to 0.
(x-3) = 0, (x-4) = 0. The last step is to put both constants after the equal sign.
x=3, x=4. Here we conclude that the values of 3 and 4 are placed in the equation would result in 0. Now, we will write the solution set in the following manner: Solution Set {3,4} A group of worksheets and advanced lessons that will help students learn how to solve quadratic equations by just factoring.

### Printable Worksheets And Lessons

- Factoring Quadratics Step-by-step Lesson- That darn zero product property again. Apply it again to this problem.
- Guided Lesson - It takes about 3-4 lengthy steps to solve these. You could complete the problems using other techniques, but we focus on factoring.
- Guided Lesson Explanation - We give you a really good strategy to use here. Comes with a full explanation.
- Practice Worksheet - Solve all the quadratics that we throw at you. See if you can isolate the variable.
- Solving Factorable Quadratic Equations Five Pack - A nice practice pack for working on and reviewing this skill.
- Matching Worksheet - Match each quadratic equation to the value of their variables.

#### Homework Sheets

There are so many different ways to solve these I didn't know where to start.

- Homework 1 - Write your answers as whole numbers or as proper or improper fractions in simplest form.
- Homework 2 - We know that the Zero Product Property states that for all real numbers a and b: If ab = 0, then a = 0 or b = 0
- Homework 3 - We will solve each of the exercises by using factorization.

#### Practice Worksheets

I tried to display a number of different methods for the solutions.

- Practice 1 - Solve and write your answers as integers or as proper or improper fractions in simplest form.
- Practice 2 - Factor the heck out of these problems. They should be easy to work with.
- Practice 3 - A nice set of practice worksheets to make it work.

#### Math Skill Quizzes

It is really important for you to show the kids deferent methods for attacking these. Hopefully, one method clicks for them.

### How This Skill Relates to Your Everyday

When we first start working with quadratic equations, they seem more like little logic puzzle that do not have any real purpose in life except to challenge us mentally. There are many applications of these types of problems and the skills that involved will help you tackle these new areas of your life with success. In the world of finance this skill is used quite often. It applies to creating business forecasts and determining the overall profit for complex organizations. In the physical world quadratics are used to predict the potential speed of a car design based on engine and body designs. It you want to track the movement of a projectile whether it be a sports ball, arrow, or even a cruise missile this is your go to math. The movement of all of these objects can be plotted out using quadratics to model it. Even in the world of electronics this skill is used to help understand the potential computing power of the chips that perform all the calculations of the device. As we continue to see, math is a very powerful tool that almost has boundless applications.