Algebra 2
Review Unit 4 / Ch.6 Polynomials
Name ______________________________
1. Write each polynomial in standard form. Then classify it by degree and by number of terms.
a. 3x  7 x  9  x
2
4
b.  3x  5 x  x  4 x  5 x
2
4
2
Standard Form: ________________________
Standard Form: ___________________________
Classify by degree __________
Classify by degree ____________
Classify by terms ________________
Classify by terms ___________________
2. Write a polynomial function with rational coefficients in FACTORED FORM with the given zeros.
Then convert Factored Form into Standard Form.
a.)
x = 6, 1, 2
b)
x = -3, 0, 1
c.
x = -2, -2, -5
3. Describe the end behaviors of the functions below.
a)
y  2 x 4  3x 2  1
b)
y  x 3  2x 2  2x  4
4. For each function, find the zeros and state the multiplicity of multiple zeros.
a.
y  ( x  4)( x  5)3
b.
y=
3s 2 ( s  4)3 ( s  2)2 ( s  1)
5. Write each polynomial in FACTORED FORM and SOLVE each equation. (Hint – find the Zeros by factoring.)
a.
( x  3)( x 2  3x  4)
b. x  2 x  x  0
3
2
6. Factor the expression using the sum or difference of cubes. (And Find the Solutions).
a. x3 – 1000
b. 27x3 + 64
7. Divide using long division.
a.
( x 3  7 x 2  5x  6)  ( x  2)
b.
(9 x 3  18x 2  x  2)  (3x  1)
8. Divide using synthetic division.
a.
( x 3  3x 2  2 x  4)  ( x  2)
b.
( x 2  3)  ( x  1)
9. Given the following polynomial functions and one of its zeros, find all the zeros/solutions of the polynomial.
a. x  6 x  11x  6  0 ;
3
2
x  2 is a zero
b. x  3x  x  3  0 ;
3
2
x  3 is a zero
x 4  23x 2  50  0
10. FACTOR completely and SOLVE.
Graph.
11.
y = (x + 4)(x - 3)(x + 2)
12.
Zeros: _______________________
Zeros: _______________________
End Behavior: ______________
End Behavior: __________________
y = (x + 5)(x – 5)(x + 3)
Use synthetic division and the Remainder Theorem to find…
13. P() if P(x) = x3  4x2 + x  2.
14.
P(3) for P(x) = 2x4  3x3  x + 4.
Use the Rational Root Theorem to list all possible rational roots for each equation.
Then find any actual roots.
15. x3 + 6x2 + x + 6 = 0