Algebra 2 – Unit 3 : Polynomial Factoring and Solving Practice Test
Name ______________________________
Date ________________
Polynomials - Simplifying
1)
15 g 8h4  18 g 8h2  15 g 5h3
3g 5h 2
1) ____________
2) (x + 4)(x2 – 3x + 2)
2) ____________
3) (5y – 3)(2y + 5)
3) ____________
4) (4x2 + 12) – (13x – 4)
4) ____________
5) (x – 12)2
5) ____________
Solving Polynomials
6) Find the solutions
16y2 – 9 = 0
6) ____________
7) Find the solutions
2x3 – 8x2 – 14x = -20
7) ____________
8) Find the real and imaginary solutions for x3 – x2 + 4x – 4 = 0
8) ___________
9) What is the value of f(x) = 7x4 – 3x3 + 8x2 + x – 9 when x = -2?
9) ___________
10) Evaluate (2 x3  3x 2  4 x  15)  ( x  3)
10) __________
11) Let f ( x)  x 4  5x3  ax 2  5x  6 , where a is an unknown real number.
If ( x  3 ) a factor of this polynomial, what is the value of a ?
11) __________
12) Using your calculator, graph of the polynomial function
x5  3x 4  19 x3  43x 2  18 x  40 . From the graph, determine
the factors of this polynomial.
12) __________
13) For the each of the graphs below:
a) State whether the function is even or odd?
Graph 1
13a) __________
Graph 2
__________
b) Is the leading coefficient positive or negative?
13b) __________
__________
c) What is the degree of the polynomial?
13c) __________
__________
d) How many real roots?
13d) __________
__________
e) How many imaginary roots?
13e) __________
__________
Graph 1
Graph 2
Solving Quadratics
14) Find the roots of x 2  144  0
14) _____________
15) Solve using any method 3(t  4)2  75
15) _____________
Complex Numbers
160
16) ______________
17) Find the absolute value of 4 – 3i
17) ______________
18) Two numbers added together give 12 – 6i. One of the
numbers is 3 – 2i. What is the other number?
18) ______________
16) Simplify
Transformation of Parent Graph
19) If y = – x2 is translated 3 left and down 1. What is the new equation? 19) ___________
A) y = – x2 + 2
B) y = – x2 – 6x – 8
C) y = – x2 – 6x – 10
D) y = – x2 + 6x + 8
Inverses
20) Which graph represents the inverse of h(x) = –3x + 6?
A)
B)
C)
20) ___________
D)
Sequences and Series
21) Find the sum of the infinite geometric series 10,
30 90 270
, ,
,....
7 49 343
21) ___________
Domain and Range
22) What is the range of y = | x – 8 | + 3?
Basic Algebra 2 – Unit 3 – Polynomial –Practice Test
22) ___________