Algebra 88 - Adding and Subtracting Polynomial Functions

The video tutorial introduces polynomial functions, explaining how they are sums of monomials. It covers the addition and subtraction of polynomial functions, providing examples and graphical representations. The tutorial also explores polynomial functions with multiple variables, demonstrating how to graph them in three dimensions. The video concludes with a preview of the next lecture on multiplying polynomials.

What is a polynomial function composed of?

• A division of monomials

• A single monomial

• A product of monomials

• The sum of one or more monomials

How do you add two polynomial functions?

• By adding their coefficients and rearranging terms

• By multiplying their coefficients

• By dividing their coefficients

• By subtracting their coefficients

What is the graphical representation of the sum of two polynomial functions?

• The product of their graphs

• The sum of their graphs

• The division of their graphs

• The difference of their graphs

What is the result of adding the polynomial functions X + 1 squared and X - 1 squared?

• A linear function

• A constant function

• A cubic function

• A parabolic function

What is the result of adding two parabolic functions?

• A linear function

• Another parabolic function

• A cubic function

• A constant function

What happens when you subtract the function F2 from F1?

• You get a cubic function

• You get a constant function

• You get a linear function

• You get a quadratic function

What is required to graph a polynomial function in two variables?

• One dimension

• Two dimensions

• Four dimensions

• Three dimensions

What shape does the graph of a two-variable second-degree polynomial function form?

• A parabola

• A line

• A circle

• A paraboloid

What is the result of adding the polynomial functions X^2 + y^2 + 2X + 1 and X^2 + y^2 - 2X + 1?

• 2X^2 + 2y^2 + 2

• X^2 + y^2

• X^2 + y^2 + 2X

• 4X^2 + 4y^2

What is the process of adding multivariable polynomial functions compared to single variable functions?

• Equally complex

• Simpler

• Equally simple

• More complex