Factorising Quadratics Flashcards

All 4 cards in this deck

What are the steps to factorise $x^2 + bx + c$?

e.g. $x^2 + 7x + 12$

1. Find two numbers with product $c$ and sum $b$: product $12$, sum $7$ gives $3$ and $4$
2. Write the brackets with those numbers: $(x+3)(x+4)$

What is the factorised form of $a^2 - b^2$ (the difference of two squares)?

$(a+b)(a-b)$, in either order.
e.g. $x^2 - y^2 = (x+y)(x-y)$

True or false? $x^2 + 9$ factorises as $(x+3)(x-3)$.

False. $(x+3)(x-3) = x^2 - 9$; a sum of two squares does not factorise.

What are the steps to factorise a difference of two squared brackets?

e.g. $(2x+3)^2 - (2x-5)^2$

1. Treat it as $A^2 - B^2 = (A+B)(A-B)$ with $A = 2x+3$, $B = 2x-5$
2. Simplify each bracket: $(4x-2)(8)$
3. Tidy the answer: $16(2x-1)$