Factorising Quadratics Worksheets
Free printable factorising quadratics worksheets with answer keys. Factorise expressions such as x² + 7x + 12 = (x + 3)(x + 4).
Using this page
Factorise expressions such as x² + 7x + 12 = (x + 3)(x + 4). Choose positive numbers only, a mix of positive and negative numbers, or the difference of two squares such as x² − 49 = (x + 7)(x − 7). Answers are given with the smaller number first. Factorising is taught in Classes 8 and 9 in India and Years 9 and 10 in Australia.
Tips
- Show the working, even when the answer seems obvious; it makes mistakes easy to spot.
- Check each answer: put it back into an equation, or estimate before working out.
- Start with the easier setting and move up once most answers are right.
- Mix one older sheet into each week so earlier skills stay fresh.
Worked example
Factorise x² + 7x + 12. Find two numbers with a product of 12 and a sum of 7. They are 3 and 4. So x² + 7x + 12 = (x + 3)(x + 4). Check: x² + 4x + 3x + 12 = x² + 7x + 12.
Common mistakes
Choosing two numbers with the right product but the wrong sum.
Getting the signs wrong. If the last term is negative, one number is positive and one is negative.
How to use this generator
Choose the options above the sheet: the number of questions and the settings for this kind of worksheet. Every change makes a new sheet straight away, and New worksheet gives a different set of questions with the same settings.
Each sheet has a worksheet number printed at the top. Type the same number later, or keep the page link, to print exactly the same questions and answer key again. Leave Answer key page ticked to print the answers on a second page, then press Print. Every printed page carries the makekite logo and web address.
Common questions
How do I check my answer?
Multiply the two brackets out. You should get back the original expression.
Can I make the sheet harder?
Yes. Use the options above the sheet: more digits, a harder level, brackets or negative numbers where they are offered.
Can I print the same worksheet again?
Yes. Note the worksheet number printed at the top, or keep the link in your browser's address bar, which ends with that number. Entering it later gives the same questions and answers.
Is it free?
Yes. There is no sign-up, and nothing you choose is sent anywhere: the sheets are made in your browser.