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

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Answer 1 · 2016-12-05T23:15:46

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

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 #x^2+14x+24# we seek two numbers such that

#"product" = 1*24 = 24#
#"sum" \ \ \ \ \ \ = 14#

So if we looks at the factors of #24# and compute their sum we get (as all the terms re positive we only need to consider positive factors);

# {: ("factor1", "factor2", "sum"),(24,1,25), (12,2,14), (6,4,10), (3,8,11) :} #

So the factors we seek are #12# and #2#

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.