Download Algebra II Honors Test Review 6-5 to 6-6

Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra II Honors Test Review 6-5 to 6-6
Short Answer
1. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation
x 3 − 10x 2 + 5x − 2 = 0. Do not find the actual roots.
2. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation
x 3 + x 2 − 7x − 4 = 0. Do not find the actual roots.
3. Find the rational roots of x 4 + 8x 3 + 7x 2 − 40x − 60 = 0.
4. A polynomial equation with rational coefficients has the roots 1 +
7, 2 −
6 . Find two additional roots.
5. Find a third-degree polynomial equation with rational coefficients that has roots –4 and 3 + i.
For the equation, find the number of complex roots, the possible number of real roots, and the possible
rational roots.
6.
x 7 − 2x 6 + 3x 2 − 2x + 5 = 0
7.
10x 7 − 10x 6 + 4 = 0
1
Name: ________________________
ID: A
Find the roots of the polynomial equation.
8. 4x 3 + 16x 2 − 22x − 10 = 0
9. x 3 − 2x 2 + 10x + 136 = 0
10. x 4 − 5x 3 + 11x 2 − 25x + 30 = 0
11. Find all zeros of 2x 4 − 3x 3 + 30x 2 − 48x − 32 = 0.
12. Find all zeros of 2x 4 − 5x 3 + 53x 2 − 125x + 75 = 0.
2
ID: A
Algebra II Honors Test Review 6-5 to 6-6
Answer Section
SHORT ANSWER
1. –2, –1, 1, 2
2. –4, –2, –1, 1, 2, 4
3. –6, –2
4. 1 − 7, 2 + 6
5. x 3 − 2x 2 − 14x + 40 = 0
6. 7 complex roots; 1, 3, 5, or 7 real roots; possible rational roots: ±1, ±5
7. 7 complex roots; 1, 3, 5, or 7 real roots; possible rational roots: ±1, ± 2, ± 4, ±
8.
−5,
1±
3
2
9. 3 ± 5i, –4
10. 2, 3, ± i 5
1
11. 2, − , ± 4i
2
3
12. 1, , ± 5i
2
1
1
1
2
4
1
, ± , ± , ± , ±
2
5
5
5
10