Download Algebra 2 - TeacherWeb

Algebra 2 - Test #5 (Practice) – Polynomial Functions
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____
1. Determine which binomial is a factor of
a. x + 5
b. x + 20
.
c. x – 24
d. x – 5
Essay
2. What are multiple zeros? Explain how you can tell if a function has multiple zeros.
Short Answer
3. Classify –3x5 – 2x3 by degree and by number of terms.
4. Classify –7x5 – 6x4 + 4x3 by degree and by number of terms.
5. Write the polynomial
in standard form.
6. Write 4x2(–2x2 + 5x3) in standard form. Then classify it by degree and number of terms.
7. Write the expression (x + 6)(x – 4) as a polynomial in standard form.
8. Write 4x3 + 8x2 – 96x in factored form.
9. Write a polynomial function in standard form with zeros at 5, –4, and 1.
10. Find the zeros of
and state the multiplicity.
Divide using synthetic division.
11.
12. Use synthetic division to find P(2) for
Factor the expression.
13.
.
14.
15.
16. Solve
. Find all complex roots.
17. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation
. Do not find the actual roots.
18. Find the rational roots of
.
Find the roots of the polynomial equation.
19.
20. A polynomial equation with rational coefficients has the roots
. Find two additional roots.
21. Find a third-degree polynomial equation with rational coefficients that has roots –5 and 6 + i.
22. Find a quadratic equation with roots –1 + 4i and –1 – 4i.
23. For the equation
roots.
, find the number of complex roots and the possible number of real
Use Pascal’s Triangle to expand the binomial.
24.
25. Use a graphing calculator to determine which type of model best fits the values in the table.
x
–6
–2
0
2
6
y
??
??
??
??
??
26. Use the TI-84 to find the zeros of
. Then sketch the graph of the equation.
27. Use a graphing calculator to find the relative minimum, relative maximum, and zeros of
. If necessary, round to the nearest hundredth.
28. The volume in cubic feet of a workshop’s storage chest can be expressed as the product of its three
dimensions:
. The depth is x + 1.
a. Find linear expressions with integer coefficients for the other dimensions.
b. If the depth of the chest is 6 feet, what are the other dimensions?
29. A manufacturer of shipping boxes has a box shaped like a cube. The side length is
5a + 4b. What is the volume of the box in terms of a and b?
30. Divide
by x + 3 using long division.
31. Solve the equation
32. Solve the equation
33. Find all the zeros of
by using a quadratic model.
Algebra 2 - Semester 1 - Test #4 (Practice)
Answer Section
MULTIPLE CHOICE
1. D
OTHER
2. If a linear factor of a polynomial is repeated, then the zero is repeated and the function has multiple zeros. To
determine whether a function has a multiple zero, factor the polynomial. If a factor is repeated in the factored
expression, then it is a multiple zero.
SHORT ANSWER
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
quintic binomial
quintic trinomial
20x5 – 8x4; quintic binomial
x2 + 2x – 24
4x(x – 4)(x + 6)
–3, multiplicity 2; 5, multiplicity 6
4
7
16.  ,
5
17. –4, –2, –1, 1, 2, 4
18. –6, –2
19. 3 ± 5i, –4
20.
21.
22.
23. 4 complex roots; 0, 2 or 4 real roots
24.
25. aa
26. 0, 3, 2
y
6
4
2
–6
–4
–2
2
4
6
x
–2
–4
–6
27. relative minimum: (0.36, –62.24), relative maximum: (–3.69, 37.79),
zeros: x = –5, –2, 2
28. a. height, x – 1; width, x – 3
b. height, 4 ft; width, 2 ft
29.
30.
, R –93
31. x
32. x
33. x