# How do you factor the trinomial #x^2+14x+24#?

##### 1 Answer

#### Explanation:

The rule to factorise any quadratic is to find two numbers such that

#"product" = x^2 " coefficient "xx" constant coefficient"#

#"sum" \ \ \ \ \ \ = x " coefficient"#

So for

#"product" = 1*24 = 24#

#"sum" \ \ \ \ \ \ = 14#

So if we looks at the factors of

So the factors we seek are

Therefore we can factorise the quadratic as follows:

#x^2+14x+24 \ \ \ \ \ = x^2 + 12 x + 2x +24 #

# :. x^2+14x+24 = x(x+12) + 2x(x+12) #

# :. x^2+14x+24 = (x+2)(x+12)#

This approach works for all quadratics (assuming it does factorise) , The middle step in the last section can usually be skipped with practice.