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Algebra II
48. CC.HSN.CN.C.8
48.4 Solving polynomials with the unknown
Finding the Unknown b in x² + bx + c
Given the factored form (x+p)(x+q), the missing coefficient b equals p plus q.
What You'll Learn
x squared + bx + c factors as (x+p)(x+q) when p plus q gives b and p times q gives c.
Given the factored form, b equals the sum of the two constants.
Example: (x+3)(x+6) gives b = 9 and c = 18.
If only c is known, list factor pairs of c and add each pair to test possible values of b.
This mirrors finding the unknown c, using the same two numbers.
What You'll Practice
1
Finding all possible k values in expressions like 3x² + kx + 4
2
Testing factor pairs with positive and negative signs
3
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:
This Unit Includes
2 Video lessons
Practice exercises
Learning resources
Skills
Trinomial Factoring
Reverse FOIL
Polynomials
Quadratic Expressions
Coefficient Finding
Factor Pairs
OH Curriculum Aligned