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Overview
Workplace and Apprenticeship Mathematics 10
Number Sense, Logical Thinking, Mathematics as a Human Endeavour
11. WA10.11
11.3 Solving polynomials with unknown constant terms
Finding the Unknown c in x² + bx + c
Given the factored form (x+p)(x+q), the missing constant c equals p times q.
What You'll Learn
x squared + bx + c factors as (x+p)(x+q) when p times q gives c and p plus q gives b.
Given the factored form, c equals the product of the two constants.
Example: (x+2)(x+5) gives c = 10 and b = 7.
The same idea works from known roots, not just a written factored form.
This mirrors finding the unknown b, using the same two numbers.
What You'll Practice
1
Finding positive constant terms by choosing number pairs that add to a sum
2
Determining negative constant terms using mixed positive and negative factors
3
Testing multiple number pair combinations to solve for unknown values
4
Verifying solutions by multiplying binomial factors back to trinomial form
Why This Matters
Solving for unknown constants in polynomials strengthens your algebraic reasoning and reverse-engineering skills. This technique is essential for advanced algebra, calculus, and solving real-world optimization problems where you need to work backward from known relationships to find missing values.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Practice exercises
Learning resources
Skills
Factoring
Trinomials
FOIL Method
Reverse FOIL
Binomials
Polynomials
Unknown Constants
Number Pairs
SK Curriculum Aligned