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Factorising method

Spot the shared factor

6x + 9
6x + 93 × 2x+3 × 33(2x + 3)

Look for something every term has in common. In 6x + 9, both terms share 3.

Detailed notes

Worked Example

Factor 6x + 9 by taking out the greatest common factor.

Step 1: Look at each term

The expression has two terms. Each term has a factor of 3.

6x + 9

Step 2: Rewrite each term using the common factor

Write both terms as 3 multiplied by something.

6x + 9=3×2x + 3×3

Step 3: Move the common factor outside

The repeated factor goes outside the bracket. The leftover parts stay inside.

3×2x + 3×3=3(2x + 3)

Step 4: Check by expanding

Multiply the 3 back in to confirm that the original expression returns.

3(2x + 3)=6x + 9