Factoring Trinomials

Learn and apply factoring trinomials using equations, examples, and interpretation.

Lesson 1 of 53 parts Practice Flashcards

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Monic Trinomials

Objective: Explain and use monic trinomials in an Algebra 1 problem.

To factor x²+bx+c as (x+m)(x+n), find m+n=b and mn=c, then expand to check. Each controls a different coefficient.

Worked examples

Try itExample 1.1: Factor x²+9x+20. What is its constant-factor pair?Show answer

4 and 5. The factor constants must add to the x coefficient and multiply to the constant. The answer is 4 and 5.

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Monic Trinomials

Objective: Explain and use monic trinomials in an Algebra 1 problem.

To factor x²+bx+c as (x+m)(x+n), find m+n=b and mn=c, then expand to check. Each controls a different coefficient.

Worked examples

Try itExample 1.1: Factor x²+9x+20. What is its constant-factor pair?Show answer

4 and 5. The factor constants must add to the x coefficient and multiply to the constant. The answer is 4 and 5.

Negative Constants

Objective: Explain and use negative constants in an Algebra 1 problem.

When c is negative in a monic trinomial, the two integer factors have opposite signs if an integer factorization exists. No, integer factors may not satisfy the required sum.

Worked examples

Try itExample 2.1: Factor x²+10x+16. What is its constant-factor pair?Show answer

2 and 8. The factor constants must add to the x coefficient and multiply to the constant. The answer is 2 and 8.

Checking Factors

Objective: Explain and use checking factors in an Algebra 1 problem.

Expand candidate binomials and compare every coefficient with the original expression; not all trinomials factor over integers. No, choose another solving method if needed.

Worked examples

Try itExample 3.1: Factor x²+14x+33. What is its constant-factor pair?Show answer

3 and 11. The factor constants must add to the x coefficient and multiply to the constant. The answer is 3 and 11.

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