Factorising Quadratics Flashcards

All 6 cards in this deck

To factorise $x^2 + bx + c$ into $(x + a)(x + d)$, what must the two numbers do?

Multiply to give $c$ and add to give $b$.
e.g. $x^2 + 4x + 3 = (x + 1)(x + 3)$

What are the steps to factorise a quadratic of the form $x^2 + bx + c$?

e.g. $x^2 + 10x + 9$

1. List pairs multiplying to $c$: $1 \times 9$, $3 \times 3$
2. Choose the pair adding to $b = 10$: $1$ and $9$
3. Write two brackets: $(x + 1)(x + 9)$

In $x^2 + bx + c$, if $c$ is negative, what signs go in the two brackets?

One $+$ and one $-$.
e.g. $x^2 + 2x - 8 = (x + 4)(x - 2)$

In $x^2 + bx + c$, if $c$ is positive and $b$ is negative, what signs go in the two brackets?

Both $-$.
e.g. $x^2 - 7x + 12 = (x - 3)(x - 4)$

How is the factorised answer written when a quadratic is a perfect square?

e.g. $x^2 + 6x + 9$

As a squared bracket: $(x + 3)^2$, or $(x + 3)(x + 3)$ — both are accepted.

True or false? To factorise $x^2 + bx + c$ you need two numbers that add to $c$ and multiply to $b$.

False.
It is the other way round: they multiply to $c$ and add to $b$.