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Grade 10
Develop algebraic reasoning and number sense
7. Multiply polynomial expressions concretely, pictorially, and symbolically
7.7 Applications of polynomials
Applications of Polynomials
Polynomials model real quantities like area and volume, letting you solve for an unknown dimension or value.
What You'll Learn
A polynomial application models a real quantity, like area or volume, as a polynomial expression.
Area from two polynomial side lengths is found by multiplying them.
Translate a word problem by naming the unknown, then writing each quantity in terms of it.
Substitute a value to evaluate, or set the polynomial equal to a target to solve for x.
Example: a garden of length x+8 and width x+5 has area x squared + 13x + 40.
What You'll Practice
1
Finding shaded areas by subtracting polynomial expressions for nested rectangles
2
Calculating circle areas using polynomial radius expressions and π
3
Applying the Pythagorean theorem to solve for variables in right triangles
4
Factoring polynomials using grouping to determine rectangle dimensions from area
5
Expanding squared binomials in area formulas and simplifying results
Why This Matters
These skills bridge algebra and geometry, preparing you for advanced math courses like trigonometry and calculus. Real-world applications include architecture, engineering design, and any field requiring spatial reasoning with variable dimensions.
Before You Start — Make Sure You Can:
This Unit Includes
7 Video lessons
Practice exercises
Learning resources
Skills
Polynomials
Area Formulas
Pythagorean Theorem
Factoring
Binomial Expansion
Geometric Applications
Expression Simplification
MB Curriculum Aligned