How to Factor Trinomials When a is 1

Factoring trinomials when the leading coefficient (a) is 1 is a straightforward process. A trinomial in this form will typically look like x² + bx + c.

To factor this trinomial, follow these steps:

1. Identify the coefficients: In the trinomial x² + bx + c, the number b is the coefficient of the middle term, and c is the constant term.
2. Look for two numbers that multiply to c and add up to b. These two numbers will help us to rewrite the trinomial in its factored form.
3. Once you have identified these two numbers, you can express the trinomial as: (x + m)(x + n), where m and n are the two numbers you found.

For example, let’s factor the trinomial x² + 5x + 6:

• Here, b = 5 and c = 6.
• We need two numbers that multiply to 6 (the constant) and add up to 5 (the coefficient of x).
• The numbers 2 and 3 fit these criteria because 2 x 3 = 6 and 2 + 3 = 5.
• Thus, we can factor the trinomial as (x + 2)(x + 3).

In summary, the process of factoring trinomials when a = 1 involves identifying suitable pairs of numbers that satisfy the multiplication and addition conditions, leading you to the product form.