Factorise and solve x2 - 8x + 15 = 0.

Factorise and solve x² - 8x + 15 = 0.

When factorising there are 3 things to look for;

1. A common factor in each component of the equation. In this case there are no common factors.

2. Whether the equation is made up of a difference of 2 squares. This is when there are only two numbers and the given equation is not a quadratic, both of the components are square numbers and one of them is subtracting the other. In this case there is not a difference of 2 squares.

3. The final thing to look for is a quadratic.

The given equation is a quadratic. The first thing to do when going about solving this is to factorise the equation i.e. put it into bracket format. To do this firstly draw 2 open brackets

(         )(          )

Secondly look at the first component of the equation which is x². Think of two things which multiply to give this with both multiples containing an x. In this case the only possile solution is two singular x's because x multiplied by x gives x². Put these two numbers as the first components in each bracket as shown below;

(x        )(x         )

The second thing to place into the brackets are two numbers which multiply to give the 3rd component in the given equation and add or subtract together to give the second component in the given equation. In this scenario the multiples of 15 are;

3, 5, 15, 1

The two which can add or subtract to give 8 are 3 and 5; these are therefore written into the open brackets;

(x       3)(x       5)

The final thing to do to complete the factorisation of this equation is to fill in the signs. To achieve a positive 15 and a negative 8 both the signs will have to be negative.

(x - 3)(x - 5)

This is the equation factorised. In the question the quadratic was equal to zero; therefore to solve this each bracket is allowed to equal zero;

(x - 3) = 0

(x - 5) = 0

If x - 3 = 0 Then x must equal 3.

If (x - 5) = 0 Then x must equal 5.

So x is equal to 3 and x is equal to 5.