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Grade 10
Develop algebraic reasoning and number sense
8. Demonstrate understanding of common factors and trinomial factoring concretely, pictorially, and symbolically
8.6 Applications of polynomials: x^2 + bx + c
Applications of Factoring x² + bx + c
Factoring a trinomial area into (x+p)(x+q) reveals the two real dimensions that produced it.
What You'll Learn
A trinomial x squared+bx+c representing area factors into two dimensions, (x+p)(x+q).
Find p and q as two numbers that multiply to c and add to b.
If the actual area is known, substitute it and solve the resulting equation for x.
Substitute the solved x back into each factor to get real length and width.
This uses the same technique as finding the unknown b or c.
What You'll Practice
1
Factoring volume expressions to find three dimensions of prisms
2
Solving cardboard box problems by identifying dimensions after cutting
3
Extracting common factors from multi-variable polynomial expressions
4
Verifying factored dimensions match given volume formulas
Why This Matters
Understanding how polynomial factoring applies to geometric problems connects abstract algebra to real-world design and engineering. You'll use these skills in physics, architecture, and manufacturing where calculating dimensions from volume or area is essential.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Practice exercises
Learning resources
Skills
Polynomial Factoring
Volume
Rectangular Prisms
Word Problems
Geometry Applications
Common Factors
Trinomials
MB Curriculum Aligned