Download Test Alg2 Chap 5N

Algebra II
Test Form N - Chapter 5
Name:
Read and follow all directions carefully. Show your work. Place answers in answer column
when is provided. Simplify all answers. NO CALCULATORS ALLOWED ON THIS PART OF
THE TEST.
Questions 1 - 2, solve by factoring.
1.
x 2  3x  28
2.
3x 2  5 x  2  0
4.
2 x2  x  4  0
Questions 3 - 4, solve by completing the square.
3.
x2  2x  5  0
Questions 5 - 6, solve by using the quadratic formula.
5.
x 2  3x  5  0
6.
6 x 2  13x  5  0
Questions 7 – 8, solve by any algebraic method. YOUR CHOICE.
7.
3  x  5   81
2
8.
x 2  8 x  48  0
Questions 9 - 12, simplify each of the following complex numbers. Place your answers in the
form of a  bi .
9.
11.
 4  i    2  5i 
 4  i  2  5i 
10.
12.
 4  i    2  5i 
4i
2  5i
9.
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10.
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11.
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12.
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Questions 13 - 15, find the value of the discriminant, the number (quantity) of roots, and type of
roots for each of the following problems. Do NOT find the solutions.
Prob
#
Equation
13
x 2  8 x  20  0
14
x2  2 x  5  0
15
x2  6 x  9  0
Value of Discriminant
# of Roots
Type of Roots
Work Space
Questions 16 - 21, factor each of the following completely. If it is not factorable, state that it is
PRIME.
16.
18.
20.
x 2  8 x  15
3 x 2  18 x
x 2  3 x  54
17.
19.
21.
x 2  12 x  36
x 2  121
5 x 2  13x  6
16.
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17.
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18.
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19.
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20.
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21.
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Questions 22 - 29, short answer.
22.
Find the value of c that makes the expression a perfect square trinomial. Then write the
expression as the square of a binomial.
a.
x2 
4
xc
9
b.
x 2  cx 
49
16
23.
Assume a quadratic equation can be solved by factoring and the roots are rational. What
is true about the value of the discriminant in the quadratic formula if the same problem
were to be solved by the quadratic formula?
24.
What is the conjugate of 3  7i ?
25.
Derive the Quadratic Formula from the standard form of the quadratic equation by
completing the square.
ax2  bx  c  0
24.
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