How do you factor the trinomial #x^2+13x+36=0#?

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Answer 1 · 2016-02-04T05:40:31

Explanation is given below

I think you mean how to solve the quadratic using factorization.

#x^2+13x+36=0#

Let us start by finding factors of #36#

#36 = 2xx18#
#36= 3xx12#
#36 = 4xx9#
#36=6xx6#

Now we need to find which pair gives the sum of #13# which is the middle term.

We can see #4+9 =13# therefore the factors of
#x^2+13x+36# is #(x+4)(x+9)#

Now solving the quadratic equation

#x^2+13x+36 = 0#
#(x+4)(x+9)=0#

By the zero product rule we get

#x+4=0# or # x+9=0#

#x=-4# or #x=-9#

The solution set would be #{-9,-4}#