Solving quadratics by factorising

Once a quadratic expression has been factorised, it can be used to solve the quadratic equation (when the expression is equal to zero).

If the product of two factors is equal to zero, then at least one of the factors must be equal to zero. This is called the zero product property.

In other words, one of the brackets needs to be zero if they need to multiply to give zero.

Factorise the left-hand side:
- (x+2)(x+3)=0
Using the zero product property, set each factor equal to zero:
- x+2=0 or x+3=0
Solve x+2=0:
- x=-2
Solve x+3=0:
- x=-3
Answer: x=-2 or x=-3.

Factorise the left-hand side:
- (x+3)(2x+1)=0
Using the zero product property, set each factor equal to zero:
- x+3=0 or 2x+1=0
Solve x+3=0:
- x=-3
Solve 2x+1=0:
- 2x=-1
- x=-\frac{1}{2}
Answer: x=-3 or x=-\frac{1}{2}.

flashcards

Question	Answer
What is the zero product property?	If the product of two factors is equal to zero, then at least one of the factors must be equal to zero.
To solve a quadratic equation by factorising, what must the expression be equal to?	Zero.
In the example solve x^2+5x+6=0, what are the two factors?	(x+2) and (x+3).
What are the solutions to x^2+5x+6=0?	x=-2 or x=-3.
In the example solve 2x^2+7x+3=0, what are the two factors?	(x+3) and (2x+1).
What are the solutions to 2x^2+7x+3=0?	x=-3 or x=-\frac{1}{2}.
After factorising a quadratic equation, what are the two steps to find the solutions?	Set each factor equal to zero using the zero product property, then solve each resulting linear equation.