Name______________________________
Date__________ Period__________
Algebra 2 – Test Chapter 6
Write each polynomial in standard form. Then classify it by degree and number of terms.
1. 9 x  2 x  3 x
2
3.
2
2. 4 x( x  5)( x  6)
Standard Form _____________
Standard Form __________
Degree ________________
Degree ________________
Terms _________________
Terms _________________
x
Y
1
91
10
95
20
260
30
365
a. Find a cubic function to model the data.
b. Find y when x is 4
Solve each equation by graphing. Where necessary, round to the nearest hundredth.
4.
y  x 3  3x 2  x  3  0
zeros: _______________
5.  x  3 x  4  0
3
zeros: ________________
6. x  6 x  1  0
2
zeros: ________________
Write a polynomial function with rational coefficients in Standard Form with the given zeros.
7. 2, 3, 5
8. -1, -1, 1
For each function, determine the zeros and their multiplicity.
9.
y  ( x  1) 2 (2 x  3) 3
10.
y  4 x 2 ( x  2) 3 ( x  1)
Name______________________________
Date__________ Period__________
Solve each equation. (Find the Zeros by Factoring)
11.
( x  1)( x 2  5 x  6)  0
12. x  10 x  16 x  0
3
2
Divide using long division.
13.
(2 x 3  13x 2  17 x  10)  ( x  5)
14.
( x 3  9 x 2  26 x  24)  ( x  4)
16.
(2 x 3  4 x  3)  ( x  1)
Divide using synthetic division.
15.
( x 3  4 x 2  x  5)  ( x  2)
17. Use synthetic division and the Remainder Theorem to find P(-5) if
P( x)   x 3  4 x 2  x  2
Name______________________________
Date__________ Period__________
Use the Rational Root Theorem to list all possible rational roots for each equation. Which Possible Solutions Work?
Extra Credit for every solution you can find.
18. x  2 x  3 x  6  0
3
2
20. Factor the expression using the sum of cubes.
19. x  3x  x  3  0
3
2
x 3 + 64
21. Factor the expression using the difference of cubes. Then solve to find all the complex roots.
x3 – 125 = 0