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 ax^{2} + bx + c = 0

All the quadratic equation worksheets in this section factorise with integer values inside each bracket.

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 form:

ax^{2} + bx + c = 0

where a, b and c are numbers, and x is an unknown.

It is also sometimes called a second degree polynomial equation.

Examples

The following equations are quadratic expressions:

x^{2} + 7x + 4

2y^{2} - 28

4a ^{2} - ½ a + 15

The following equations are NOT quadratic expressions:

x^{3} + 7x + 4

2y - 28

4a ^{5} - ½ a + 15

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).

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.

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 x
^{2}, gradually getting harder. - Sheet 9 - mixed quadratic equations with 2x
^{2}, either both brackets positive or both negative - Sheets 10 to 11 - mixed quadratic equations with more than one x
^{2}

Section 1: Beginning Section

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.

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!

If you are looking for a fun printable algebra game to play then try out our algebra game page.

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The only equipment you need is a scientific calculator, some dice, and a few counters!

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