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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 ax 2 + bx + c = 0

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

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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:

ax 2 + 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.

The following ARE quadratic equations in standard form:

• x 2 + 7x + 4 = 0
• z 2 - 25 = 0
• 2w 2 + 7w = 0
• 2y 2 - 28 = 0
• 4a 2 - ½ a + 15 = 0

The following ARE quadratic equations but not yet in standard form:

• can be rewritten as x 2 + 6x - 4 = 0 (which is in standard form)
• can be rewritten as 3n 2 - 6n - 10 = 0 (which is in standard form)

The following are NOT quadratic equations:

• x 3 + 7x + 4 = 0 (because of the x 3 )
• 2y - 28 = 0 (because there is no y 2 term)
• 4a 5 - 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 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

• Factorising Quadratic Equations 1
• PDF version
• Factorising Quadratic Equations 2
• Factorising Quadratic Equations 3
• Factorising Quadratic Equations 4

Section 2: Intermediate

• Factorising Quadratic Equations 5
• Factorising Quadratic Equations 6
• Factorising Quadratic Equations 7
• Factorising Quadratic Equations 8

Section 3: Advanced

• Factorising Quadratic Equations 9
• Factorising Quadratic Equations 10
• Factorising Quadratic Equations 11

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!

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 Worksheets
• 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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Factorising into a Single Bracket: Worksheets with Answers

Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers.

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Factorising polynomials (linear, quadratic and cubic) worksheet (with solutions)

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

19 May 2024

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A worksheet on factorising polynomials covering different cases: extracting a common factor, difference of two squares, perfect square, quadratic factorisation. Detailed solutions are provided.

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Factorising polynomials worksheets (with solutions)

Three worksheets on factorising polynomials covering different cases: extracting a common factor, difference of two squares, perfect square, quadratic factorisation. Detailed solutions are provided. From https://placeformath.blogspot.com/p/worksheet-shop.html

Algebra Bundle (7 worksheets with solutions)

A collection of ten worksheets on the following algebra topics: Changing the subject of a formula, equation of a straight line ( finding the gradient of a line given its equation, finding the equation of a line given its gradient and one point on it or two points on it and finding the equation of a line parallel to another line passing through a given point), expanding expressions by multiplying brackets by a single number or variable and collecting like terms when appropriate, factorising polynomials (extracting a common factor, difference of two squares, perfect square, quadratic factorisation), indices, inverse and composite functions, linear equations. Detailed solutions are included.

GCSE Algebra Bundle (Expanding and factorising expressions)

A collection of 10 worksheets on expanding brackets and factorising algebraic expressions including the cases of perfect squares and difference of two squares. Detailed solutions are included. Good for GCSE/IGCE students. From https://mathamaniacs.com/

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