Factoring Trinomials

Factoring trinomials is a fundamental concept in algebra. A trinomial is a polynomial with three terms. When factoring trinomials, we are looking for a way to express the trinomial as a product of two binomials. The process involves finding two binomials that, when multiplied together, produce the original trinomial.

Steps for Factoring Trinomials

1. Identify the type of trinomial: Trinomials can be of the form ax² + bx + c, where a, b, and c are constants.
2. Find two numbers that multiply to a * c and add to b: Look for two numbers that, when multiplied, give a * c and when added, give b.
3. Split the middle term: Rewrite the middle term bx as the two numbers found in step 2.
4. Factor by grouping: Group the terms and factor using the distributive property.
5. Write the factored form: Express the original trinomial as a product of two binomials.

Example

Let's factor the trinomial x² + 5x + 6:

1. Identify the type of trinomial: This is a trinomial of the form ax² + bx + c with a = 1, b = 5, and c = 6.
2. Find two numbers: We need two numbers that multiply to 1 * 6 = 6 and add to 5. These numbers are 2 and 3.
3. Split the middle term: Rewrite the middle term as 2x + 3x.
4. Factor by grouping: Group the terms and factor using the distributive property:
   x² + 2x + 3x + 6
   x(x + 2) + 3(x + 2)
   (x + 2)(x + 3)
5. Write the factored form: The factored form of the trinomial is (x + 2)(x + 3).

Study Guide

When factoring trinomials, it's important to remember the following key points:

• Identify the type of trinomial: Determine the coefficients a, b, and c in the trinomial ax² + bx + c.
• Find two numbers: Look for two numbers that multiply to a * c and add to b.
• Split the middle term: Rewrite the middle term as the two numbers found in the previous step.
• Factor by grouping: Group the terms and factor using the distributive property.
• Write the factored form: Express the original trinomial as a product of two binomials.

Practice factoring trinomials with different coefficients and signs to strengthen your understanding of the concept.

Remember to check your factored form by multiplying the two binomials to ensure they produce the original trinomial.

Factoring trinomials is a valuable skill in algebra, as it is used in various applications, including solving quadratic equations and simplifying expressions.

By mastering factoring trinomials, you will build a strong foundation for more advanced algebraic concepts.