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Grade 12 Advanced Functions, University Preparation (MHF4U)
C. Polynomial and Rational Functions
31. 12AF.C1.6
31.1 Solving polynomial equations
Solving Polynomial Equations
Solve polynomial equations by setting them to zero, factoring, and applying the zero product property.
What You'll Learn
A polynomial equation sets a polynomial equal to zero; its solutions are the roots.
The zero product property: if a product is zero, at least one factor is zero.
Steps: set to zero, factor, set each factor to zero, then solve each.
Example: x squared minus 5x plus 6 = 0 factors to (x-2)(x-3)=0, so x=2 or x=3.
Higher-degree equations are solved the same way once fully factored.
What You'll Practice
1
Solving simple quadratic equations by isolating and square rooting both sides
2
Factoring trinomials and applying zero product property to find x-values
3
Working with equations requiring GCF extraction before solving
4
Avoiding common errors like dividing out variables and losing solutions
Why This Matters
Solving polynomial equations is essential for algebra, calculus, physics, and engineering. Whether you're calculating projectile motion, optimizing business problems, or modeling real-world scenarios, these solving techniques form the foundation for advanced mathematics and practical applications.
This Unit Includes
4 Video lessons
Practice exercises
Learning resources
Skills
Polynomial Equations
Factoring
Zero Product Property
Quadratic Equations
Isolating Variables
Square Roots
Algebraic Solving
ON Curriculum Aligned