Factoring Quadratic Equations
Worksheets

$Math Problem Worksheets Captain Salamander$

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.

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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 Equations Help

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

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Section 2: Intermediate

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$quadratic equation problem factorising quadratic equations 6$

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$quadratic equations worksheet factorising quadratic equations 8$

Section 3: Advanced

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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.

Factorising Quadratic Equations Help

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.

$6th Grade Distributive Property image$

6th Grade Distributive Property Worksheets

$Expressions and Equations 6th Grade image$

Expressions and Equations 6th Grade

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

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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!

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