Name: ___________________________________________ Period: __________
Unit 5: Polynomials
Section 5.1: Introduction to Polynomials
Write each polynomial in standard form. Then classify it by degree and number of terms.
1.
5.
2.
6.
3.
7.
4.
8.
Factor the polynomial.
13.
16.
14.
17.
15.
18.
Find the zeros of each function. State the multiplicity of multiple zeros.
21.
23.
25.
26.
22.
24.
Section 5.2: Synthetic Division
Divide.
1.
2.
3.
4.
5.
Determine whether each binomial is a factor of
11.
12.
Section 5.3: Solving +/- of Cubes
Solve each equation.
1.
2.
3.
4.
5.
6.
Algebra 2
Homework
9.
10.
11.
12.
19.
20.
6.
7.
8.
9.
10.
.
13.
14.
7.
8.
9.
Section 5.4: Solving Polynomials
DAY 1
Solve each equation. State the number of solutions, the possible number of complex or irrational solutions, the possible
number of real solutions, the possible number of positive solutions, the possible number of negative solution, and all the
possible rational solutions.
1.
9.
2.
10.
3.
11.
4.
12.
13.
5.
14.
6.
15.
7.
8.
16.
Section 5.4: Solving Polynomials
DAY 2
Solve each equation. State the number of solutions, the possible number of complex or irrational solutions, the possible
number of real solutions, the possible number of positive solutions, the possible number of negative solution, and all the
possible rational solutions.
1.
9.
2.
10.
3.
11.
4.
12.
5.
13.
6.
14.
7.
15.
8.
16.
Section 5.5: Writing Equations from Roots
Write an equation given the following zeros.
1. 5, 6, 7
3. -5, -5, 1
2. -2, 0, 1
4. 1, -1, -2, 4
5. 3, 0 with a multiplicity of 2
6. -2, 3 with a multiplicity of 2
Find a third degree polynomial with the following roots.
7. 3, 2-i
9. 5, 2i
8. -1, 3+i
10. -7,
11. 2,
12. 1,
Unit 5 Review
Write the polynomial in standard form and classify by degree and number of terms.
3.
1.
4.
2.
Write each polynomial in factored form.
5.
6.
Find a polynomial with the given degree with the given roots.
7. Fourth degree; -1, 4, and 2i
9. Third degree; 4 and
8. Third degree; -3, 2, and 6
10. Third degree; -2 and
Solve each equation. State the number of solutions, the possible number of complex or irrational solutions, the possible
number of real solutions, the possible number of positive solutions, the possible number of negative solution, and all the
possible rational solutions.
11.
16.
12.
17.
13.
18.
19.
14.
20.
15.
21. If a polynomial equation with real coefficients has -4i and 4-2i among its roots, then what two other roots must
it have?
22. If a polynomial equation with real coefficients has
roots must it have?
and
among its roots, then what two other