5.1 Polynomial Operations Review

Summary of Adding and Subtracting Polynomials
In the video, the rules for adding and subtracting polynomials were reviewed. When adding or subtracting polynomials, it is essential to combine like terms and watch out for subtraction problems where distribution may be needed. Results should be written in standard form, with terms decreasing in degree.

Addition of Polynomials
Problem 1: Ignoring parentheses, combine like terms:
(3x^2 + 1x^2 = 4x^2)
(11x - 5x = 6x)
(4 - 13 = 9)
Subtraction of Polynomials
Problem 2: Handling subtraction problems:
(-4n^2 - 2n^2 = -6n^2)
(2n + n = 3n)
(-10 + 7 = -3)
Dealing with Parentheses
Problem 3: Addressing subtraction within parentheses:
(5k - 3r - 2k^2 + 2k = -4k^2 + 0k + 7)
(-1 - 2y^2 + 5y + y^3 = -2y^2 + 6y - 3)
Conclusion
The video further demonstrated how to multiply polynomials by distributing or using FOIL method, combine like terms, and write answers in standard form. Subsequently, division of polynomials was touched upon with an emphasis on the distributive property, followed by a practical example to derive the area of a trapezoid algebraically. Overall, the video review provided a comprehensive overview of adding, subtracting, multiplying, and dividing polynomials.