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