Solving polynomials with the unknown

What You'll Learn

Identify all possible values of the coefficient b in trinomials ax² + bx + c

Apply reverse FOIL method to determine factor pairs that produce given polynomials

Recognize how different factor combinations yield different middle term coefficients

Calculate b by multiplying outer and inner terms and adding the results

What You'll Practice

Finding all possible k values in expressions like 3x² + kx + 4

Testing factor pairs with positive and negative signs

Switching factor positions to find additional solutions

Why This Matters

Finding the unknown coefficient b strengthens your understanding of how trinomial factoring works in reverse. This skill is essential for verifying factored forms, solving quadratic equations, and building flexibility with polynomial manipulation in algebra and beyond.

Before You Start — Make Sure You Can:

Multiplying binomial by binomial Common factors of polynomials Solving polynomials with unknown coefficients

This Unit Includes

2 Video lessons

Practice exercises

Skills

Trinomial Factoring

Reverse FOIL

Polynomials

Quadratic Expressions

Coefficient Finding

Factor Pairs

OH Curriculum Aligned