Practice Set 1
10 Foundational Questions
This set focuses on degree, leading coefficient, end behavior, zeros, y-intercepts, and recognizing factored or expanded form.
Practice Questions
DOK 1 Practice Set: Polynomial Foundations
Use Desmos as a quick support tool while you identify basic polynomial features and check your thinking.
Question 1
What is the degree of f(x) = 3x⁴ - 2x² + 7?
Desmos Move: Type y = 3x⁴ - 2x² + 7. The shape can support your answer, but the highest exponent gives the degree right away.
Question 2
What is the leading coefficient of g(x) = -2x³ + 5x - 1?
Desmos Move: Graph y = -2x³ + 5x - 1 to notice the right side falls, which matches a negative leading coefficient for an odd-degree polynomial.
Question 3
A polynomial has degree 3 and a positive leading coefficient. Which end behavior is correct?
Desmos Move: In Desmos, graph y = x³ as a quick model. It falls on the left and rises on the right.
Question 4
Which set lists all zeros of the graph shown?
Use the x-axis crossing points to identify the zeros.
Desmos Move: In Desmos, trace where the graph crosses the x-axis. Those x-values are the zeros.
Question 5
What is the y-intercept of h(x) = x² - 4x + 3?
Desmos Move: Type y = x² - 4x + 3 in Desmos and look where the graph crosses the y-axis. That happens when x = 0.
Question 6
Which expression is written in factored form?
Desmos Move: Graph the factored expression in Desmos and connect each factor to an x-intercept.
Question 7
Which expression is written in expanded form?
Desmos Move: If you expand the factored choices in Desmos or by hand, you can compare them to the standard expanded form.
Question 8
If p(x) = (x + 2)(x - 5), what are the zeros of p(x)?
Desmos Move: Enter y = (x + 2)(x - 5) and check where the graph meets the x-axis to confirm the zeros.
Question 9
What is the y-intercept of the graph shown?
The y-intercept is where the graph crosses the y-axis.
Desmos Move: In Desmos, the y-intercept is where the graph crosses the y-axis. That point always has x = 0.
Question 10
How many x-intercepts does q(x) = (x - 1)(x + 3)(x - 4) have?
Desmos Move: Graph y = (x - 1)(x + 3)(x - 4) in Desmos and count how many times it crosses the x-axis.