DOK 2 Practice Set: Polynomial Connections

Use Desmos to check structure, compare forms, and confirm how zeros connect to graph behavior in multi-step polynomial questions.

Practice Set 2

10 Connected Questions

This set focuses on polynomial operations, factoring, zeros, end behavior, and interpreting graphs or equations in EOC-style review.

10 questionsDOK 2 review

Question 1

Which expression is equivalent to (2x³ - 3x² + 4x - 1) + (x³ + 5x² - 6x + 7)?

DOK 2

Desmos Move: Enter each polynomial and add them carefully term by term. Matching powers of x should be combined.

Question 2

Which polynomial is equivalent to (x - 3)(x + 2)?

DOK 2

Desmos Move: Graph both the factored form and each answer choice in Desmos. Equivalent expressions will create the same graph.

Question 3

Which expression is the correct factored form of x² - 5x - 24?

DOK 2

Desmos Move: Check the x-intercepts of y = x² - 5x - 24 in Desmos. The factors should match those zeros.

Question 4

For f(x) = (x + 4)(x - 1)², which statement is true?

DOK 2

Desmos Move: Graph the function and watch what happens at each x-intercept. A double zero usually touches and turns.

Question 5

Which equation could match the graph shown?

DOK 2

Notice where the graph touches the x-axis and where it crosses.

Desmos Move: Use the graph to identify where the polynomial touches or crosses the x-axis. That tells you which zero has even multiplicity.

Question 6

What is the end behavior of g(x) = -2x⁴ + 3x² - 1?

DOK 2

Desmos Move: The highest-degree term controls the end behavior. A negative even-degree term behaves like -2x⁴.

Question 7

What is the greatest zero of p(x) = x³ - x² - 6x?

DOK 2

Numeric response

Desmos Move: Factor out x first, then factor what remains. You can also graph the function and trace the x-intercepts.

Question 8

Which equation could represent the graph shown?

DOK 2

Use the intercepts and end behavior together to choose the equation.

Desmos Move: Read the x-intercepts first, then use the end behavior to decide whether the leading coefficient should be positive or negative.

Question 9

How many real zeros does h(x) = x⁴ - 5x² + 4 have?

DOK 2

Numeric response

Desmos Move: Treat x² like one variable first. You can also graph the function to count the x-axis intersections.

Question 10

Which statement best describes q(x) = -(x - 2)²(x + 5)?

DOK 2

Desmos Move: A squared factor usually means the graph touches and turns. Because this is a negative cubic, the graph rises left and falls right.