How do you factor y=x^2 + 35x + 36 ?

2 Answers
Dec 27, 2015

You can not factor that trinomial, unfortunately.

Explanation:

You can always see if a quadratic function like the one above is factorable by using the discriminant of the quadratic formula:

b^2 - 4ac
35^2 - 4(1)(36)
1120 - 144
976

Since the final result, 976, is not a perfect square, this trinomial cannot be factored into even factors.

Hopefully you understand now.

Dec 27, 2015

This quadratic can only be factored using irrational coefficients:

x^2+35x+36

=(x+35/2-sqrt(1081)/2)(x+35/2+sqrt(1081)/2)

Explanation:

The difference of squares identity can be written:

a^2-b^2 = (a-b)(a+b)

So:

x^2+35x+36

=x^2+35x+(35/2)^2-(35/2)^2+36

=(x+35/2)^2-1225/4+144/4

=(x+35/2)^2-1081/4

=(x+35/2)^2-(sqrt(1081)/2)^2

=((x+35/2)-sqrt(1081)/2)((x+35/2)+sqrt(1081)/2)

=(x+35/2-sqrt(1081)/2)(x+35/2+sqrt(1081)/2)

We cannot simplify sqrt(1081) further since 1081=23*47 has no square factors.