TOPIC
MY PROGRESS
Pug Score
0%
Best Streak
0 in a row
Study Points
+0
Overview
Practice
Watch
Read
Quiz
Next Steps
Get Started
Get unlimited access to all videos, practice problems, and study tools.
Unlimited practice
Full videos
Back to Menu
Topic Progress
Pug Score
0%
Videos Watched
0/0
Best Practice
No score
Read
Not viewed
Best Quiz
No attempts
Best Streak
0 in a row
Study Points
+0
Overview
Practice
Watch
Read
Quiz
Next Steps
Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
C. Polynomial and Rational Functions
32. 12AF.C1.7
32.3 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
ON Curriculum Aligned