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Solving by factorisation

Factorisation means rewriting a quadratic equation as a product of two simpler expressions and then using the zero product principle.

In one line: Find the pair, split the middle, solve the two brackets.

Practice This Concept

Understand it

This method works best when the quadratic can be split into factors with neat numbers. After factorising, each factor is set to zero, which gives the roots quickly.

Example

x² - 7x + 12 = 0 becomes (x - 3)(x - 4) = 0.

Formula and rule

If ax² + bx + c = (px + q)(rx + s), then solve by setting each factor equal to zero.

Use the zero product principle after factorisation.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

Solve x² - 9x + 20 = 0.

1We need two numbers whose product is 20 and sum is -9, which are -4 and -5.
2So x² - 9x + 20 = (x - 4)(x - 5) = 0, giving x = 4 or x = 5.

Method you can reuse

1Write the equation in standard form.
2Find two numbers with the correct product and sum.
3Split the middle term or directly factorise.
4Set each factor equal to zero.
5Write the roots.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why does factorisation help in solving a quadratic equation quickly?

Think first, then show answer

Because it turns one quadratic equation into two simple linear factors. Then each factor can be set equal to zero, which gives the roots without using a long formula.

Common wrong answer

Writing (x - 2)(x - 10) for x² - 12x + 20 = 0.

Why it loses marks: The sum does not match -12.

Don't mix this up

Students often choose the wrong factor pair because they match only the product and ignore the middle term.

Exam tip

Check both the product and the sum while choosing factor pairs, especially for negative middle terms.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

CBSE often asks for solving by factorisation when the quadratic has simple factors and neat roots.

1
Enough for 1 mark
Factorisation means rewriting a quadratic equation as a product of two simpler expressions and then using the zero product principle.
2
Add for 2 marks
Example: x² - 7x + 12 = 0 becomes (x - 3)(x - 4) = 0.
3
Add for 3 marks
This method works best when the quadratic can be split into factors with neat numbers.

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