AlgebraKey Stage 3

Taking out a common algebraic factor

Take out the common number and the smallest shared powers of each letter.

  • Find the highest common numerical factor first.
  • For each letter present in every term, use its smallest power.
  • Divide every term by the complete factor and keep the signs.

Example 1

Factorise fully. Take out , using the smallest shared powers.

Each term must contain the complete common factor.

Example 2

Factorise fully. Take out , using the smallest shared powers.

Each term must contain the complete common factor.

Remember
Only take out a letter if it occurs in every term. If a term equals the whole common factor, it leaves inside the bracket.

Your turn

Question 1

Factorise fully.

Check answer
Take out , using the smallest shared powers.Each term must contain the complete common factor.
Question 2

Factorise fully.

Check answer
Take out , using the smallest shared powers.Each term must contain the complete common factor.
Question 3

Factorise fully.

Check answer
Take out , using the smallest shared powers.Each term must contain the complete common factor.
Question 4

Factorise fully.

Check answer
Take out , using the smallest shared powers.Each term must contain the complete common factor.
Question 5

Factorise fully.

Check answer
Take out , using the smallest shared powers.Each term must contain the complete common factor.
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Taking out a common numerical factorFactorising three or more terms into one bracket