Factorising Simple Quadratics Flashcards

All 5 cards in this deck

To factorise $x^2 + bx + c$ as $(x + p)(x + q)$, what must $p$ and $q$ satisfy?

$p + q = b$ and $pq = c$.

e.g. for $x^2 + 5x + 6$ the numbers add to $5$ and multiply to $6$.

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

e.g. $x^2 + 5x + 6$

1. Find two numbers with product $c$ and sum $b$: product $6$, sum $5$ → $2$ and $3$
2. Put them in brackets with $x$: $(x + 2)(x + 3)$

True or false? To factorise $x^2 + 5x + 6$ the two numbers must add to $6$ and multiply to $5$.

False. It is the other way round: the sum must be $5$ and the product must be $6$.

In $x^2 + bx + c$ with $c$ negative, what are the signs of the two numbers in the brackets?

One positive and one negative.

e.g. $x^2 + 3x - 10 = (x + 5)(x - 2)$

In $x^2 + bx + c$ with $c$ positive and $b$ negative, what are the signs of the two numbers in the brackets?

Both negative.

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