Factorising Out Terms Flashcards

All 5 cards in this deck

What does the instruction "factorise fully" tell you to do?

Take out the highest common factor of all the terms, so nothing more can be taken out.
e.g. $9x^2 + 6x = 3x(3x + 2)$, not $3(3x^2 + 2x)$

What are the steps to factorise fully an expression with a common factor?

e.g. $15w^2 - 5w$

1. Find the HCF of the numbers: $5$
2. Find the highest power of the letter in every term: $w$, so the HCF is $5w$
3. Divide each term by it and bracket: $5w(3w - 1)$

True or false? $2(2a + 12)$ is a fully factorised form of $4a + 24$.

False.
The HCF is $4$, so the fully factorised answer is $4(a + 6)$.

How can you check that you have factorised an expression correctly?

Expand the brackets again — you should get back the original expression.

True or false? An expression like $x^2 + 7x$, with no number term, can always be factorised by taking out $x$.

True.
Every term contains $x$, so $x^2 + 7x = x(x + 7)$.