Practice 29 Solving Polynomial Equations
1. Given f (x) = 3x3 + 7x2 – 13x – 5,
a) Divide f (x) by (3x + 1).
Name:_________________________
4. Graph 𝑦 = −2 log 3(𝑥 + 5)
b) What is the complete factorization of f (x)?
5. Graph 𝑦 = log 3 (𝑥 + 3) − 1
c) What are the roots of f (x)?
d) What are the solutions to
3x3 + 7x2 – 13x – 5 = 0?
2. Which expression is equivalent to the
following expression if no denominators
2x
1
2
x

1
equal zero?
2x
1
2x 1
x-intercept:_____ y-intercept:_____
D: _________________
R: _________________
Asymptote(s): _________________
End Behavior: __________________
6. Simplify:
3. Find all zeros of y = 5x3  5x.
x3 x2

x2 1 x 1
7. Solve over the Complex Numbers using the
graph below: x5  3x4  8x3  8x2  9x  5 = 0
8. Graph 𝑦 = 3𝑥−2 − 4
Asymptote(s): _________________
9.
3
2
10. Find all the zeros using the given zero: g ( x)  x  5 x  5 x  4 , x  4
11.
12. Divide: (3x3 – 5x + 1) ÷ (x – 3)
13.
14. Find all factors of x3 – x2 – 5x – 3 given that (x + 1) is a factor.
15. Graph 𝑦 = log 2 (−𝑥 ) + 3
16. Solve: 𝑥 2 + 6𝑥 = 10
17. Solve: (4𝑥 + 5)2 = 64
Asymptote(s): _________________
18.
19. Find all roots of x3 + 4x = 2x2 + 8
2
25.
26. Find all roots to y = 0 given y  x 3  6 x 2  x  6
20. Find all zeros of 2𝑥 + 3 = −4𝑥
27.
21. State the zeros of the following function and
give their multiplicity. y = x2 (x + 5) (x – 4)3
y
3

28. Simplify y  4 4  y
2 x 3  7 x 2  11x  5
2x 1
22. Divide
29. Graph 𝑦 = 3 log 5 (𝑥 − 2) + 1
23.
24. Find all solutions to f(x) = 0 given
f ( x)  x 4  3x 2  4 .
Asymptote(s): _________________
30. Graph:
y  2  ( x  4)  6
32.
33.
Domain: _________________________
Range: __________________________
Zero(s): __________________
x-intercept(s): __________________
y-intercept(s): __________________
Increasing Interval(s): __________________
Decreasing Interval(s): __________________
End Behavior
As x   , y approaches ______
As x   , y approaches ______
31. Graph 𝑦 = 212−3𝑥 + 1
Asymptote(s): _________________