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.