Quiz Review 5.1-5.2
Worksheet
Name______________________________________
Write each polynomial in standard form. Then classify it by degree and by number of terms.
1. 4𝑥 4 + 6𝑥 3 − 2 − 𝑥 4
What is the degree of the polynomial
that generates the given data?
4.
2. 9𝑡 2 − 2𝑡 + 3𝑡 2
3. 4𝑥(𝑥 − 5)(𝑥 + 6)
Answer each question(a-e).
5.
Sign of leading coefficient is negative
Odd degree
Zero at -2 with multiplicity of 2
Zero at 1 with multiplicity of 1
These are the only zeros
Y intercept is at 4
a. Sketch the graph:
b. Write an equation in factored form:
c. Find the relative maximum and minimum
d. State where the graph is increasing and decreasing
e. State the number of turning points
Determine the end behavior of the graph of each polynomial function.
6. 𝑦 = 3𝑥 − 2𝑥 2 − 4
7. 𝑦 = 4𝑥 3 − 7𝑥 + 2
Factor each polynomial.
8.
3𝑥 4 − 18𝑥 3 − 2𝑥 + 12
9.
4𝑥 3 − 28𝑥 2 + 40𝑥
10.
𝑥 4 − 81
Fill in the information for each polynomial and use it to sketch the graph.
11. y  xx  7
2
2
12. y  2(3x  2) ( x  2)
2
Zeros
Multiplicity
Cross/touch
Zeros
Multiplicity
4
3
2
13. y  x  12 x  35x
Cross/touch
Zeros
Multiplicity
y-intercept:
y-intercept:
y-intercept:
Degree:
Degree:
Degree:
End behavior:
End behavior:
End behavior:
Cross/touch
14. What are the relative maximum & minimums of the function (𝑥) = 𝑥 4 − 4𝑥 2 ? Round to the nearest
hundredth.
Write the polynomial function with the given zeros in standard form.
15.
-3, 2, and 3.
16.
-4, 4, 0, 0
17. The width of a box is 2m less than the height. The length is 5m less than the height.
a.) Write polynomial to represent the volume V (h)
b.) What is the maximum volume?