Factoring Trinomials Formula
Before going to learn the factoring trinomials formulas, let us recall what is a trinomial. A trinomial is a polynomial with three terms. Factoring means writing an expression as the product of two or more expressions. A trinomial can be a perfect square or a nonperfect square. Let us learn the factoring trinomials formulas along with a few solved examples.
What Are Factoring Trinomials Formulas?
A trinomial can be a perfect square or a nonperfect square. We have two formulas to factorize a perfect square trinomial. But for factorizing a nonperfect square trinomial, we do not have any specific formula, instead, we have a process.
 The factoring trinomials formulas of perfect square trinomials are:
a^{2} + 2ab + b^{2} = (a + b)^{2}
a^{2}  2ab + b^{2} = (a  b)^{2}
For applying either of these formulas, the trinomial should be one of the forms a^{2} + 2ab + b^{2} (or) a^{2}  2ab + b^{2}.
 The process of factoring a nonperfect trinomial ax^{2} + bx + c is:
Step 1: Find ac and identify b.
Step 2: Find two numbers whose product is ac and whose sum is b.
Step 3: Split the middle term as the sum of two terms using the numbers from step  2.
Step 4: Factor by grouping.
Let us see the applications of factoring trinomials formulas in the following section.
Solved Examples Using Factoring Trinomials Formulas

Example 1: Factor x^{2}  16x + 64 using the factoring trinomials formulas.
Solution:
We can write the given trinomial as,
x^{2}  16x + 64 = x^{2}  2(x)(8) + 8^{2}
The right side trinomial is of the form a^{2}  2ab + b^{2} and hence we can apply the formula,
a^{2}  2ab + b^{2} = (a  b)^{2}
Thus, x^{2}  2(x)(8) + 8^{2} = (x  8)^{2}
Answer: x^{2}  16x + 64 = (x  8)^{2}.

Example 2 : Factor the trinomial 2x^{2}  x  3.
Solution:
We use the factoring trinomial formula of nonperfect trinomials to factor the given trinomial.
Comparing 2x^{2}  x  3 with ax^{2} + bx + c, we get a = 2, b = 1, and c = 3.
Here ac = 2(3) = 6 and b = 1.
Two numbers whose product is 6 and whose sum is 1 are 3 and 2.
We will split the middle term x as 3x + 2x and then we factor by grouping the terms.
2x^{2}  x  3
= 2x^{2}  3x + 2x  3
= x (2x  3) + 1 (2x  3)
= (2x  3)(x + 1)
Answer: 2x^{2}  x  3 = (2x  3)(x + 1).