Quadratics Factorising Methods Flashcards

All 5 cards in this deck

What are the steps to factorise $ax^2 + bx + c$ by splitting the middle term?

e.g. $2x^2 + 7x + 3$

1. Find two numbers with product $ac$ and sum $b$: product $6$, sum $7$ gives $6$ and $1$
2. Split the middle term: $2x^2 + 6x + x + 3$
3. Factorise in pairs: $2x(x+3) + 1(x+3) = (x+3)(2x+1)$

What should you always check for before trying to factorise a quadratic into two brackets?

e.g. $2x^2 + 10x + 12$

A common factor of all three terms — take it out first.
e.g. $2(x^2+5x+6) = 2(x+2)(x+3)$

What are the steps to factorise a two-variable quadratic?

e.g. $3x^2 - 5xy - 2y^2$

1. Each bracket has an $x$ term and a $y$ term: $(3x\ \ )(x\ \ )$
2. Find the $y$ terms whose product gives $-2y^2$ and whose cross terms give $-5xy$: $+y$ and $-2y$
3. Answer: $(3x+y)(x-2y)$

True or false? In $x^2 + bx + c$ with $c$ positive and $b$ negative, both numbers in the brackets are negative.

True. Two negatives multiply to a positive $c$ and add to a negative $b$.

How do you check a factorisation is correct?

e.g. you claim $2x^2+7x+3 = (x+3)(2x+1)$

Expand the brackets and check you get back the original expression.
e.g. $(x+3)(2x+1) = 2x^2+x+6x+3 = 2x^2+7x+3$ ✓