Polynomial Multiplication in the Real World
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Objective
I can construct a polynomial function to model a real-world scenario and analyze its behavior using multiplication.
Part 1 of 4
Warm-up video
Katie Kelly · 24:10
We don't generate video — this one is by Katie Kelly on YouTube. The practice questions and exit ticket below were drafted by AI for this objective, and every question is editable in the teacher guide.
Part 2 of 4
Key concepts
3 concepts
- 1
When multiplying monomials, you can use the commutative property to rearrange terms and then add the exponents of like bases: 4x * 5x = 20x².
- 2
To multiply a monomial by a polynomial, use the distributive property to multiply the monomial by each term inside the polynomial: 4x(2x² + 7x + 3) = 8x³ + 28x² + 12x.
- 3
When multiplying (2x - 1)(7x + 6), use distributive property to multiply each term in the first binomial by each term in the second, then combine like terms to simplify: 14x² + 12x - 7x - 6 = 14x² + 5x - 6.
Part 3 of 4
Practice
3 questions
A rectangular garden has a length of (x + 7) meters and a width of (2x - 3) meters. Write a polynomial function, A(x), that represents the area of the garden. Then, determine the area of the garden if x = 5 meters.
A construction company is designing a storage unit. The dimensions are given by the polynomials (x + 2), (x + 3), and (2x - 1). Write a polynomial V(x) that represents the volume of the storage unit. What is the leading coefficient and degree of V(x)?
Part 4 of 4
Exit ticket
Quick comprehension check
“The dimensions of a rectangular garden are (2x + 3) feet and (x - 1) feet. Write an expression that represents the area of the garden.”
Sample answer included in the free materials
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