Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra II Honors Test Review 6-1 to 6-4
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Use a graphing calculator to determine which type of model best fits the values in the table.
x
–6
–2
0
2
6
y
–6
–2
0
2
6
a.
b.
quadratic model
cubic model
c.
d.
linear model
none of these
2. Determine which binomial is not a factor of 4x 4 − 21x 3 − 46x 2 + 219x + 180.
a. x + 4
c. x – 5
b. x + 3
d. 4x + 3
3. The volume of a shipping box in cubic feet can be expressed as the polynomial 2x 3 + 11x 2 + 17x + 6. Each
dimension of the box can be expressed as a linear expression with integer coefficients. Which expression could
represent one of the three dimensions of the box?
a. x + 6
c. 2x + 3
b. x + 1
d. 2x + 1
Short Answer
4. Zach wrote the formula w(w – 1)(5w + 4) for the volume of a rectangular prism he is designing, with width w,
which is always has a positive value greater than 1. Find the product and then classify this polynomial by degree
and by number of terms.
5. Write the polynomial
6x 2 − 9x 3 + 3
in standard form.
3
6. Write 4x2(–2x2 + 5x3) in standard form. Then classify it by degree and number of terms.
1
Name: ________________________
ID: A
7. The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1995. Find a cubic
function to model the data and use it to estimate the number of cottonwoods planted in 2006.
Years since 1995
Trees planted (in thousands)
1
3
5
7
9
1.3
18.3
70.5
177.1
357.3
8. Write the expression (x + 6)(x – 4) as a polynomial in standard form.
9. Write 4x3 + 8x2 – 96x in factored form.
10. Miguel is designing shipping boxes that are rectangular prisms. One shape of box with height h in feet, has a
volume defined by the function V(h) = h(h − 10)(h − 8). Graph the function. What is the maximum volume for
the domain 0 < h < 10? Round to the nearest cubic foot.
11. Use a graphing calculator to find the relative minimum, relative maximum, and zeros of
y = 3x 3 + 15x 2 − 12x − 60. If necessary, round to the nearest hundredth.
12. Find the zeros of y = x(x − 3)(x − 2). Then graph the equation.
13. Write a polynomial function in standard form with zeros at 5, –4, and 1.
2
Name: ________________________
ID: A
14. Find the zeros of f(x) = (x + 3) 2 (x − 5) 6 and state the multiplicity.
15. Divide 3x 3 − 3x 2 − 4x + 3 by x + 3.
Divide using synthetic division.
16. (x 4 + 15x 3 − 77x 2 + 13x − 36) ÷ (x − 4)
Solve the equation by graphing.
17. x 2 + 7x + 19 = 0
18. The dimensions in inches of a shipping box at We Ship 4 You can be expressed as width x, length x + 5, and
height 3x – 1. The volume is about 7.6 ft3. Find the dimensions of the box in inches. Round to the nearest inch.
19. Over two summers, Ray saved $1000 and $600. The polynomial 1000x 2 + 600x represents her savings after three
years, where x is the growth factor. (The interest rate r is x – 1.) What is the interest rate she needs to save $1850
after three years?
Factor the expression.
20. x 3 + 216
21. x 4 − 20x 2 + 64
2
Name: ________________________
ID: A
22. Solve 125x 3 + 343 = 0. Find all complex roots.
23. Ian designed a child’s tent in the shape of a cube. The volume of the tent in cubic feet can be modeled by the
equation s 3 − 64 = 0, where s is the side length. What is the side length of the tent?
24. Solve x 4 − 34x 2 = −225.
25. The volume in cubic feet of a workshop’s storage chest can be expressed as the product of its three dimensions:
V(x) = x 3 − 3x 2 − x + 3. 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?
4
ID: A
Algebra II Honors Test Review 6-1 to 6-4
Answer Section
MULTIPLE CHOICE
1. C
2. A
3. D
SHORT ANSWER
5w 3 − w 2 − 4w; cubic trinomial
2x 2 − 3x 3 + 1
20x5 – 8x4; quintic binomial
T(x) = 0.4x 3 + 0.8x 2 + 0.1x; 630.3 thousand trees
x2 + 2x – 24
4x(x – 4)(x + 6)
105 ft3
relative minimum: (0.36, –62.24), relative maximum: (–3.69, 37.79),
zeros: x = –5, –2, 2
12. 0, 3, 2
4.
5.
6.
7.
8.
9.
10.
11.
13.
14.
15.
16.
17.
18.
19.
20.
21.
f(x) = x 3 − 2x 2 − 19x + 20
–3, multiplicity 2; 5, multiplicity 6
3x 2 − 12x + 32, R –93
x 3 + 19x 2 − x + 9
no solution
15 in. by 20 in. by 44 in.
9.3%
(x + 6)(x 2 − 6x + 36)
(x − 2)(x + 2)(x − 4)(x + 4)
1
ID: A
7 35 ± 35i 3
22. − ,
5
50
23. 4 feet
24. 3, –3, 5, –5
25. a. height, x – 1; width, x – 3
b. height, 4 ft; width, 2 ft
2