# Factorising quadratics - (easy) Example 1

Factorise the quadratic `x^2+7x+10`

Therefore the factors of 10 are:

1 and 10

2 and 5

Now ask yourself what factors of `c` add to give `b`.

i.e. what factors of 10 equal 7.

`5times2=10` `5+2=7`

Therefore:

`x^2+7x+10`

Can be written as:

`(x+2)(x+5)`

Check by multiplying out:

The shock is that `(x+2)(x+5)` also gives you the roots of `x^2+7x+10=0`

Separate the brackets and put them equal to zero.

`x+2=0`

And `x+5=0`

Now solve for `x`

Therefore `x=-2` and `x=-5`

**Answer:**

The roots of `x^2+7x+10=0` are `x=-2` and `x=-5`

**NOTE:**

This example has also been used in completing the square examples and quadratic formula examples to show that the roots `-2` and `-5` can be found using any of these methods.

# Factorising quadratics - (easy) Example 1

Factorise the quadratic `x^2+7x+10`

Therefore the factors of 10 are:

1 and 10

2 and 5

Now ask yourself what factors of `c` add to give `b`.

i.e. what factors of 10 equal 7.

`5times2=10` `5+2=7`

Therefore:

`x^2+7x+10`

Can be written as:

`(x+2)(x+5)`

Check by multiplying out:

The shock is that `(x+2)(x+5)` also gives you the roots of `x^2+7x+10=0`

Separate the brackets and put them equal to zero.

`x+2=0`

And `x+5=0`

Now solve for `x`

Therefore `x=-2` and `x=-5`

**Answer:**

The roots of `x^2+7x+10=0` are `x=-2` and `x=-5`

**NOTE:**

This example has also been used in completing the square examples and quadratic formula examples to show that the roots `-2` and `-5` can be found using any of these methods.