Algebra 83 - Polynomials

Professor Von Schmohawk introduces polynomial functions, explaining their structure, components, and applications in various fields. The lecture covers monomials, polynomial structure, and general notation, emphasizing the importance of exponents and coefficients. It also discusses polynomial functions and their graphical representations, highlighting the differences between linear, quadratic, and higher-degree polynomials.

What type of graph does a linear function have?

• A parabola

• A circle

• A line

• A hyperbola

What is a monomial?

• A sum of multiple terms

• A single term with a variable and a coefficient

• A constant without a variable

• A polynomial with two terms

In a polynomial, what is the term with the highest exponent called?

• The trailing term

• The middle term

• The leading term

• The constant term

What determines the degree of a polynomial?

• The number of terms

• The largest coefficient

• The smallest exponent

• The highest exponent

Which of the following is not allowed in polynomial exponents?

• Real numbers

• Negative integers

• Positive integers

• Zero

What is the general form of a polynomial's leading term?

• a sub 1 times x to the first power

• a sub n times x to the 0 power

• a sub n times x to the nth power

• a sub 0 times x to the 0 power

In general notation, what can the constants in a polynomial be?

• Only integers

• Any real number

• Only negative numbers

• Only positive numbers

What is a zero degree polynomial function?

• A linear function

• A quadratic function

• A constant function

• A cubic function

What type of graph does a quadratic function have?

• A line

• A hyperbola

• A circle

• A parabola

How are higher degree polynomial functions described?

• Simple and predictable

• Complex and varied

• Always linear

• Always quadratic