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 non-perfect 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 non-perfect square. We have two formulas to factorize a perfect square trinomial. But for factorizing a non-perfect square trinomial, we do not have any specific formula, instead, we have a process.
The factoring trinomials formulas of perfect square trinomials are:
a2 + 2ab + b2 = (a + b)2
a2 - 2ab + b2 = (a - b)2
For applying either of these formulas, the trinomial should be one of the forms a2 + 2ab + b2 (or) a2 - 2ab + b2.
The process of factoring a non-perfect trinomial ax2 + 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.
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