Chapter 12.7
Applications of polynomials
What You'll Learn
Apply polynomial operations to calculate areas of geometric shapes like rectangles and circles
Use the Pythagorean theorem with polynomial expressions to find unknown dimensions
Subtract polynomial area expressions to find shaded regions between overlapping shapes
Factor polynomials to determine dimensions when given total area
Expand binomial and trinomial expressions to simplify geometric formulas
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
Skills
Polynomials
Area Formulas
Pythagorean Theorem
Factoring
Binomial Expansion
Geometric Applications
Expression Simplification
