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Factoring Quadratic Equations
Worksheets
Welcome to the Math Salamanders' Factoring Quadratic Equations Worksheets.
Here you will find a range of worksheets to help you to
learn to factorise a range of different quadratic equations of the form ax2 + bx + c = 0
All the quadratic equation worksheets in this section factorise with integer values inside each bracket.
There is also a quick quiz at the bottom of the page where you can test your skill online and get immediate feedback!
Factoring Quadratic Equations Worksheets
Definition of a Quadratic Equation
A quadratic equation is an equation involving the square of a number which is the highest power in the equation.
It is usually in the standard form:
ax2 + bx + c = 0
where a, b and c are numbers, and x is an unknown. The variable a cannot be 0 (but b and c can be 0)
Note that the operations can be '+' or '-'.
It is also sometimes called a second degree polynomial equation.
Examples
The following ARE quadratic equations in standard form:
- x2 + 7x + 4 = 0
- z2 - 25 = 0
- 2w2 + 7w = 0
- 2y2 - 28 = 0
- 4a 2 - ½ a + 15 = 0
The following ARE quadratic equations but not yet in standard form:
-
x2 + 6x = 4
- can be rewritten as x2 + 6x - 4 = 0 (which is in standard form)
-
3n2 - 10 = 6n
- can be rewritten as 3n2 - 6n - 10 = 0 (which is in standard form)
The following are NOT quadratic equations:
- x3 + 7x + 4 = 0 (because of the x3)
- 2y - 28 = 0 (because there is no y2 term)
- 4a5 - ½ a + 15 = 0 (because a has been raised to the 5th power)
How to solve a quadratic equation
There are 2 main methods to use when solving a quadratic equation:
1) The factoring method - this is used for paticular cases when the solution involves integers or fractions
2) The formula method - this can be used for any quadratic equation
The worksheets on this page are designed to be solved using the factoring method (though you could use the formula method to solve the equations if you wish).
Factorising Quadratic Equations Support
If you need help learning to factorise a quadratic equation then we have a help page waiting for you!
The page will show you step-by-step how to go about factoring a quadratic equation.
Factorising Quadratic Equation Worksheets
The sheets are arranged in order of difficulty to help introduce you into more complicated examples gradually.
- Sheets 1 & 2 - positive values inside each bracket only
- Sheet 3 - negative values inside each bracket only
- Sheet 4 - one positive and one negative value in the brackets.
- Sheets 5 to 8 - mixed quadratic equations with one x2, gradually getting harder.
- Sheet 9 - mixed quadratic equations with 2x2, either both brackets positive or both negative
- Sheets 10 to 11 - mixed quadratic equations with more than one x2
Section 1: Beginning Section
Section 2: Intermediate
Section 3: Advanced
Factorising Quadratic Equations Walkthrough Video
This short video walkthrough shows several problems from our Factorising Quadratic Equations Worksheet 5 being solved and has been produced by the West Explains Best math channel.
If you would like some support in solving the problems on these sheets, please check out the video below!
Factorising Quadratic Equations Support
If you need help learning to factorise a quadratic equation then we have a help page waiting for you!
The page will show you step-by-step how to go about factoring a quadratic equation.
Looking for some easier algebra worksheets
We have a range of easier algebra worksheets designed for 6th graders.
These worksheets involve working with simpler equations and expressions than those on this page.
More Recommended Math Worksheets
Take a look at some more of our worksheets similar to these.
Free Algebra Problem Solver
The Mathway Calculator is a great way to solve algebra problems that you can type into a calculator.
Try using this online calculator tool to solve one of your problems and watch it work!
There are a range of calculators to choose from to meet your needs.
The Mathway problem solver will answer your problem instantly and also give you a link to view each of the steps needed.
If you choose to 'View the steps' you will be directed to the Mathway website where you will be able to see in more detail each of the steps needed to solve the problem. Please note that Mathway may charge you a small fee for this!
Algebra Math Games
If you are looking for a fun printable algebra game to play then try out our algebra game page.
You will find a range of algebra games that make learning algebra fun and non-threatening.
The only equipment you need is a scientific calculator, some dice, and a few counters!
Factoring Quadratic Equations Quiz
These quick quizzes test your knowledge and skill at solving quadratic equations.
We have an easier quiz where the coefficient of the x squared term is 1 and integer solutions only.
We have a harder quiz with integer and fractional answers and the coefficient of the x squared term has different values.
The link below will open the quiz in a dedicated quiz page or you can preview a copy of the quiz underneath.
Our quizzes have been created using Google Forms.
At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.
This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.
For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.
We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.
We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.
For more information on the information we collect, please take a look at our Privacy Policy
We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.
Factorising Quadratic Equations Quiz 1 (Easier)
This factoring quadratic equations quiz helps you to factor and solve a range of basic quadratic equations with integer solutions.
Factorising Quadratic Equations Quiz 2 (Harder)
This factoring quadratic equations quiz helps you to factor and solve a range of harder quadratic equations with integer and fraction solutions.
How to Print or Save these sheets 🖶
Need help with printing or saving?
Follow these 3 steps to get your worksheets printed perfectly!
How to Print or Save these sheets 🖶
Need help with printing or saving?
Follow these 3 steps to get your worksheets printed perfectly!
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Math-Salamanders.com
The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.
If you have any questions or need any information about our site, please get in touch with us using the 'Contact Us' tab at the top and bottom of every page.
