Check to see if the constant in either the first or third term of the trinomial is a prime number. A prime number can be divided evenly only by itself and 1, so there is only one possible pair of binomial factors.br>


For example, in x2 + 6x + 5, "5 is a prime number, so the binomial must be in the form (__ 5)(__ 1).

In the problem 3x2+10x+8, 3 is a prime number, so the binomial must be in the form (3x __)(x __).
For the problem 3x2+4x+1, both 3 and 1 are prime numbers, so the only possible solution is (3x+1)(x+1). (You should still multiply this out to check your work, since some expressions can't be factored at all – for example, 3x2+100x+1 has no factors.)

, A perfect square trinomial can be factored into two identical binomials, and the factor is usually written (x+1)2 instead of (x+1)(x+1). Here a few common ones that tend to show up in problems:


x2+2x+1=(x+1)2, and x2-2x+1=(x-1)2

x2+4x+4=(x+2)2, and x2-4x+4=(x-2)2

x2+6x+9=(x+3)2, and x2-6x+9=(x-3)2

A perfect square trinomial in the form ax2 + bx + c always has a and c terms that are positive perfect squares (such as 1, 4, 9, 16, or 25), and a b term (positive or negative) that equals 2(√a * √c)., Not all trinomials can be factored. If you're stuck on a quadratic trinomials (ax2+bx+c), use the quadratic formula to find the answer. If the only answers are the square root of a negative number, no real solutions exist, so there are no factors.


For non-quadratic trinomials, use Eisenstein's Criterion, described in the Tips section.
Check for prime numbers.
Check to see if the trinomial is a perfect square.
Check whether no solution exists.
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