1. Write y = (x ? 6)(x ? 4)(x + 2) in standard form.
? ? ? ?
y = x3 + 48
y = x3 ? 8x2 + 4x + 48 y = x3 ? 2x2 + 4x ? 8 y = x3 ? 8x2 ? 8x + 24 2. Factor x4 ? 8x2 + 15.
? ? ? ?
(x? 3)2(x ? 5)2
(x ? 3)(x + 3)(x ? 5)(x + 5) (x ? (x ?
)(x + )2(x ?
)(x ? )2
)(x +
)
3. Solve x3 + 5x2 ? 9x ? 45 = 0 by graphing.
? ? ? ?
5, 3 ?5, ?3, 3 ?3, 5, 3 ?5, 9
4. Evaluate .
? ? ? ?
60,480 504 84
5. Find the roots of x3 + 4x2 + 3x + 12 = 0.
? x = ?4, ±i
? ? ?
x = ?4,
x = ?4, ±3i x = 4, ±i
6. Classify 2x3 ? 2x by degree and by number of terms.
? ? ? ?
cubic monomial quadratic binomial cubic binomial cubic trinomial
7. Divide (5x3 ? 6 ? 5x) ÷ (10 + 5x) using synthetic division.
? ? ? ?
x2 ? 2x + 3, R 24 x2 ? 3x, R 44 x2 ? 2x + 3, R ?36 x2 ? 3x, R ?56
8. Use a graphing calculator to find a polynomial function to model the data.
? ? ? ?
f(x) = 4.68x3 + 8.87x2 + 4.25x + 6.32 f(x) = 4.68x2 + 8.87x + 6.32
f(x) = ?4.68x3 ? 8.87x2 ? 4.25x ? 6.32 f(x) = 0.4468x3 + 8.87x2 + 4.25x + 6.32 9. Factor 3q3 ? 81.
? ? ?
3(q ? 3)(q2 + 3q + 9) (q + 3)(q2 + 3q + 9) ?3(q ? 3)(q2 + 3q + 9)
? (q ? 3)(q2 + 3q + 9)
10. The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1987. Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in 1998.
? ? ? ?
T(x) = 0.3x3 + 0.3x + 0.4; 167.2 thousand trees T(x) = 0.3x3 + 0.3x2 + 0.1x + 0.1; 167.2 thousand trees T(x) = 0.1x3 + 0.3x2 + 0.3x + 0.1; 172.8 thousand trees T(x) = 0.1x3 + 0.1x + 0.4; 172.8 thousand trees 11. Solve x4 ? 17x2 + 16 = 0.
? ? ? ?
x = ±1, ±2i x = ±1, ±4 x = ±1, ±4i x = ±1, ±2
12. If no digit appears more than once, how many 3-digit numbers can be formed from the digits 2, 4, 5, 7, and 9?
? ? ? ?
60 numbers 10 numbers 5 numbers 25 numbers
13. Evaluate .
? ?
14,190 4
? ?
8555
14. Evaluate .
? ? ? ?
99 110 55 77
15. Assume red and green are equally likely occurrences. What is the probability that you will get zero green lights in a row of five lights?
? ? ? ?
16. Write a polynomial in standard form with zeros ?3, ?6, and ?1.
? ? ? ?
x3 + 10x2 + 27x + 18 = 0 x3 ? 10x2 ? 27x ? 18 = 0 x3 ? 2x2 + 21x + 18 = 0 x3 ? 4x2 + 9x + 18 = 0
17. Divide (x4 ? 11x3 ? 49x2 + 899x ? 2506) ÷ (x ? 8).
? ? ? ?
x3 ? 3x2 ? 24x ? 584, R ?14 x3 ? 3x2 + 73x + 315, R ?1483 x3 + 8x2 ? 24x ? 584, R 1483 x3 ? 3x2 ? 73x + 315, R 14
18. A fifth-degree polynomial equation with rational coefficients has the roots 2, ?7i, and ?7 + i. Find the remaining roots.
? 7i, ?7 + i
? ? ?
?2, 7i, ?7 ? i 7i, ?7 ? i ?7i, 7 ? i
19. Find only the rational roots of 4x3 ? 3x ? 1 = 0.
? ? ? ?
?1, 1, ?
,
±1, ±±1
20. Evaluate 9P8.
? ? ? ?
181,440 72 1 362,880