Practice Set 6
10 Polynomial Readiness Questions
This final mixed set checks whether you can move between direct skill questions, graph reasoning, tables, and factor-based equation work with steady accuracy.
Practice Questions
Mixed DOK Practice Set C: Polynomial Readiness Check
Finish with a balanced review of polynomial features, factoring, graph behavior, and equation building before moving into full EOC review.
Question 1
Which statement is true for f(x) = 2x³ - 5x?
Desmos Move: Graph the function to confirm the end behavior, but use the leading term 2x³ to answer quickly.
Question 2
For p(x) = x³ + mx² - 11x + 28, if (x - 4) is a factor, what is the value of m?
Desmos Move: A factor of (x - 4) means p(4) = 0. Substitute x = 4, solve for m, then graph the finished polynomial to check the zero.
Question 3
Which equation could model the table of values shown?
| x | -1 | 0 | 2 | 3 |
|---|---|---|---|---|
| p(x) | 0 | 6 | 0 | 0 |
Match the zero outputs first, then use the y-intercept to check the scale factor.
Desmos Move: Start by identifying the zeros from the table, then use the y-intercept to confirm the scale factor.
Question 4
A graph touches the x-axis at x = -2 and crosses the x-axis at x = 1. Which least-degree equation could model the graph?
One zero is a bounce and the other is a cross, so the multiplicities are different.
Desmos Move: A touch means even multiplicity, while a cross means odd multiplicity. Graph the choices if you want a quick visual check.
Question 5
The least-degree polynomial with zeros -1, 2, and 2 can be written as f(x) = a(x + 1)(x - 2)². If f(0) = 12, what is the value of a?
Desmos Move: Use the y-intercept by substituting x = 0. That gives a one-step equation for the scale factor.
Question 6
Which expression is the complete factorization over the real numbers of x⁴ - 5x² - 36?
Desmos Move: Treat the expression like a quadratic in x² first. After that, factor any real quadratic factor you can still break apart.
Question 7
A polynomial has degree 5 and a positive leading coefficient. Which statement must be true?
Desmos Move: Use two facts together: a degree-n polynomial can have at most n - 1 turning points, and a positive odd degree falls left and rises right.
Question 8
A polynomial can be written as p(x) = a(x + 3)(x - 1)(x - 2). If p(4) = 84, what is the value of a?
Desmos Move: Substitute x = 4 into the factored form and use the given output to solve for a.
Question 9
A polynomial has zeros at x = -2 and x = 3, and the graph touches the x-axis at x = 3. Which factored form could represent the least-degree polynomial?
Desmos Move: Use the zeros to build the factors, then square the factor whose zero is a touch instead of a cross.
Question 10
A student says, "If a polynomial graph has 3 turning points, the degree must be 3." Which response is best?
Desmos Move: Remember the turning point rule: degree n means at most n - 1 turning points. Work backward from the graph behavior.