Factorising Out Terms Flashcards

All 5 cards in this deck

How do you find the common factor to take out of an algebraic expression?

e.g. $15x^3 + 3x^2y$

Take the HCF of the number parts and the lowest power of each letter appearing in every term.

Here: $3x^2(5x + y)$

What are the steps to factorise by taking out a common factor?

e.g. $6x^2 + 15x$

1. HCF of the numbers: $3$
2. Lowest power of $x$ in every term: $x$, so factor is $3x$
3. Divide each term by $3x$: $3x(2x + 5)$

True or false? $x(9x + 6)$ is a full factorisation of $9x^2 + 6x$.

False. The bracket still has a common factor of $3$; the full factorisation is $3x(3x + 2)$.

How do you factorise an expression with a bracketed common factor?

e.g. $(x + y)^2 + 3(x + y)$

Treat the whole bracket as the common factor and take it out.

Here: $(x + y)(x + y + 3)$

True or false? When the common factor you take out is equal to one of the terms, that term becomes $1$ inside the bracket.

True.

e.g. $6x + 6 = 6(x + 1)$