Operations with Polynomials: A Comprehensive Review

This video tutorial covers Chapter 5 on polynomials, focusing on operations with polynomials and exponent rules. It reviews multiplying, dividing, and simplifying monomials, as well as adding, subtracting, and multiplying polynomials. The tutorial explains key concepts like the degree of a polynomial and provides examples to illustrate the properties of exponents. It also includes exercises for students to practice simplifying expressions and performing polynomial operations.

What are the two main objectives of Chapter 5?

• To study the properties of logarithms and their applications

• To multiply, divide, and simplify monomials and expressions involving powers; and to add, subtract, and multiply polynomials

• To understand quadratic equations and their solutions

• To learn about linear equations and inequalities

What is the result of multiplying 3 squared by 3 to the fourth?

• 3 to the eighth

• 3 to the seventh

• 3 to the fifth

• 3 to the sixth

How do you handle a negative exponent?

• Add the exponent to the base

• Subtract the exponent from the base

• Take the reciprocal of the base raised to the positive exponent

• Multiply the base by the exponent

What is the simplified form of 9 to the fifth divided by 9 squared?

• 9 to the fourth

• 9 to the third

• 9 to the second

• 9 to the seventh

What is a monomial?

• A polynomial with three terms

• A variable with a negative exponent

• A polynomial with two terms

• A number, variable, or product of variables with non-negative integer exponents

Which of the following is NOT a polynomial?

• C to the fourth minus four times the square root of C plus 18

• Negative 16 P to the 3/4 plus 3/4 P squared Q to the seventh

• 3x squared plus 2x minus 5

• 5y cubed minus 3y plus 7

What is the degree of the polynomial 3x^2 + 2x^3 - 5?

• 5

• 1

• 3

• 2

How do you simplify the expression 2a squared plus 5a minus 7 minus (a cubed minus 3a plus 2)?

• Negative a cubed minus 8a plus 9

• Negative a cubed plus 8a minus 9

• a cubed plus 8a minus 9

• a cubed minus 8a plus 9

What is the result of adding 4x squared plus negative 2x squared and negative 9x plus negative 5x?

• 2x squared plus 14x

• Negative 2x squared plus 14x

• Negative 2x squared minus 14x

• 2x squared minus 14x

What is the result of multiplying negative Y by the polynomial 4y squared minus 2y plus 3?

• Negative 4y cubed plus 2y squared minus 3y

• Negative 4y cubed minus 2y squared plus 3y

• 4y cubed minus 2y squared plus 3y

• 4y cubed plus 2y squared minus 3y