W12 Polynomial Test Review
Topics on the Test
Simplify Exponents
Rational Root
Find the roots of 5 x 5  2 x 4  8 x 3  11x  8 using the p and q and guess and check
Write an equation and solve for it to be equal to a value.
Word Problem
Long division
(5x 4  14 x3  9 x)  ( x 2  3x)
Synthetic division
( x3  28x  48)  ( x  4)
3x3  2 x 2  6 x  4
2 x 4  3x 2  1
Factor group
Factor variable
substitution
Sum/Diff Cubes
4 x3  16 x 2  x  4
16 x 4  8 x 2  1
3
Factor 8 x  81
Write the polynomial function with real coefficients and roots of 7i and 9.
Write Polynomial
equation
Graph Polynomial
Graph with correct end behavior, roots and y-intercept f ( x)  x3  3x 2  4 x  12
Review Problems
2 x3  6 x 2  8 x
x2  4x
1. Simplify:
2. Divide the following polynomials:
3. Find all the zeros (including imaginary)
x 5  4 x 3  45 x
5. divide these two polynomials.
(3x3  59 x  44)  ( x  4)
7. Solve for the roots of this polynomial.
y= 3x3  2 x 2  9 x  6
9. Solve this polynomial.
y= 5 x 4  31x 2  6
4. Divide these two polynomials.
(4 x 4  10 x3  9 x 2  x  1)  ( x 2  3x)
6. Factor this polynomial completely.
81x 4  1
8. Factor this polynomial completely.
24 x 4  3 x
10. Find the real zeros of this polynomial
f ( x)  x 3  6 x  5
11. Find all the zeros of this polynomial and graph
f ( x)  x3  3x 2  4 x  12
13. The sides of a square are lengthened so that the new
sides are 5 more than twice the original side:
a) Find the polynomial that represents the perimeter.
b) Find the polynomial that represents the area.
15. Simplify
12. Describe the end behavior and sketch the graph of
f ( x)   x 5  x 3  12 x
14. Solve this polynomial equation and graph
x 4  13x 2  36  0
a)
x 2  2 x  2 2 x 4  3x 3  5 x  1
16.Write the equation of the polynomial graphed
b)


17. Divide 3x 4  4 x3  30 x  5  x  3
18. Factor each polynomial COMPLETELY
a) 18 y 4  15 y 3  3 y 2
b) 3x 3  27 x 2  4 x  36
19. Write the polynomial function of third degree that has real coefficients, the given zeros, and a leading
3iare
,3i,5
coefficient of 2. Zeros
2-3i and 5
20. . Find the roots and sketch the function f ( x)  x 4  14 x 3  65 x 2  102 x where one root is x = 6. Accurately plot the roots and y- intercept.