Exploring Operations with Polynomials

This video tutorial covers section 4.3 on operations with polynomials, including addition, subtraction, and multiplication. It explains how to determine if an expression is a polynomial, the degree, and the leading coefficient. The tutorial introduces the box method for organizing polynomial multiplication and applies these concepts to a practical problem involving urban development. The video concludes with a fun fact about the instructor's favorite superhero.

Which of the following is NOT a polynomial?

• x^3 - 4x + 5

• 5x^4 - 3x^2 + 7

• 2x^2 + 3x + 1

• 1/x + 2

What is the degree of the polynomial 3x^3 + 2x^2 - x + 4?

• 3

• 2

• 4

• 1

When adding the polynomials 2x^2 + 3x and x^2 - x + 4, what is the resulting polynomial?

• x^2 + 2x + 4

• 2x^2 + 2x + 4

• 3x^2 + 2x + 4

• 3x^2 + 4x + 4

What must you remember to do when subtracting polynomials?

• Distribute the subtraction to all terms

• Add the exponents

• Combine like terms

• Multiply the coefficients

What is the product of (x + 2)(x - 3) using the FOIL method?

• x^2 - x - 6

• x^2 + x - 6

• x^2 - 6

• x^2 - 5

Using the formula (a - b)^2, what is the expanded form of (x - 5)^2?

• x^2 - 10x + 25

• x^2 + 10x + 25

• x^2 - 25

• x^2 + 25

What is the result of multiplying 3x by (2x^2 - 4x + 5)?

• 6x^2 - 12x + 15

• 6x^3 - 4x + 5

• 6x^3 - 12x + 15

• 6x^3 - 12x^2 + 15x

In the box method, what is the product of 2x and 3x^2?

• 6x^3

• 5x^3

• 6x^2

• 5x^2

What is the radius of a circular base if the sidewalk around it is 12 feet wide and the total area is 1206 square feet?

• 7.59 feet

• 8.59 feet

• 10.59 feet

• 9.59 feet

If the radius of a circular base is 7.59 feet, what is the diameter?

• 15.18 feet

• 14.18 feet

• 16.18 feet

• 13.18 feet