Polynomial Operations and Properties

This video tutorial covers the basics of polynomials, including how to classify them based on their degree and number of terms. It also explains how to simplify algebraic expressions by combining like terms and using distribution. The tutorial further explores simplifying products and solving word problems involving exponents and radicals. Key concepts include understanding polynomial classification, simplifying expressions, and applying distribution in multiplication.

What is the first step in putting polynomials in standard form?

• Arrange terms alphabetically

• Arrange terms by degree of the variable

• Arrange terms by coefficient size

• Arrange terms by constant value

Which of the following is a quadratic trinomial?

• x^3 + 2x + 1

• 2x^2 + 3x + 4

• x + 5

• 3x^2

How do you identify a linear binomial?

• It has four terms and the highest degree is 1

• It has one term and the highest degree is 3

• It has three terms and the highest degree is 2

• It has two terms and the highest degree is 1

What is the result of combining like terms in the expression 5x + 5x?

• 0

• 10x

• 25x

• 5x

When distributing a negative sign across parentheses, what happens to the terms inside?

• Their signs are reversed

• They remain unchanged

• They are multiplied by zero

• They are added together

What is the simplified form of 2z * (z + 5)?

• 2z^2 + 10z

• 2z + 5z

• 2z^2 + 5

• z^2 + 10z

In a triangle with sides 5x, 2x, and a missing side, if the perimeter is 16x + 3, what is the missing side?

• 9x - 1

• 9x + 1

• 7x - 1

• 7x + 1

How do you simplify the expression 3x * 5x?

• 15x

• 15x^2

• 8x

• 8x^2

What is the result of multiplying 3x by 5y?

• 15xy

• 15x^2

• 15y^2

• 15x

What is the simplified form of the expression 3√7 * 5√2?

• 15√14

• 15√9

• 15√7

• 15√2