Practice Set 4
10 Mixed Polynomial Questions
This set mixes easy, medium, and challenging questions about operations, factoring, zeros, graph behavior, and polynomial models.
Practice Questions
Mixed Practice Set A: Polynomial Functions
Move between quick checks, graph reading, and modeling so you can practice the same kind of switching the EOC expects.
Question 1
Which statement is true for f(x) = -3x⁴ + 2x² - x + 7?
Desmos Move: Graph the function to notice both ends fall, but use the highest exponent and its coefficient to answer quickly.
Question 2
Which expression is equivalent to (4x³ + x² - 6x + 8) - (x³ - 5x² + 2x - 3)?
Desmos Move: Subtract each matching term carefully. It helps to think of the second polynomial as being added with opposite signs.
Question 3
Which polynomial is equivalent to (x - 5)(x + 2)?
Desmos Move: You can multiply by hand or graph the factored form and each answer choice in Desmos to see which expressions match exactly.
Question 4
Which expression is the correct factored form of x² + x - 12?
Desmos Move: Look for two numbers that multiply to -12 and add to 1. Desmos can confirm the zeros after you factor.
Question 5
If q(x) = (x + 3)(x - 1)(x - 4), which set lists all x-intercepts of the graph of q?
Desmos Move: Set each factor equal to 0, or graph the function and look for where it crosses the x-axis.
Question 6
Which statement is true for g(x) = -x²(x - 3)(x + 1)?
Desmos Move: Use the degree and leading coefficient for end behavior, then use multiplicity to decide whether the graph crosses or touches at each zero.
Question 7
Which equation could match the graph shown?
Watch for the bounce at one zero and the crossings at the others.
Desmos Move: Read the intercepts first, then notice where the graph touches instead of crossing. End behavior helps confirm the sign of the leading coefficient.
Question 8
A school club models profit with P(x) = -(x - 8)(x - 40), where x is the number of snack boxes sold. Which conclusion best matches the model?
Desmos Move: Graph the model and use the x-intercepts as break-even points. The vertex halfway between them shows the maximum profit.
Question 9
Which equation could represent the table of values shown?
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | 0 | -6 | -8 | -6 | 0 |
Use the zeros and the sign of the outputs between them to choose the best equation.
Desmos Move: The table gives zeros at x = -2 and x = 2. Then check the sign of the outputs between the zeros to decide whether the parabola opens up or down.
Question 10
A least-degree polynomial can be written as f(x) = a(x + 1)(x - 3)². If the graph passes through (0, -18), what is the value of a?
Desmos Move: Use the given point by substituting x = 0 and y = -18. Then solve for the missing scale factor a and graph the result to confirm.