Factoring Quadratic Equations

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.

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 form:

ax2 + 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.


The following equations are quadratic expressions:

x2 + 7x + 4

2y2 - 28

4a 2 - ½ a + 15

The following equations are NOT quadratic expressions:

x3 + 7x + 4

2y - 28

4a 5 - ½ a + 15

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 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.

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