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Regents Factoring & Roots Questions
By Jeanmarie Mullen
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Last updated almost 5 years ago
24 questions
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Question 1
1.
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Question 2
2.
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Question 3
3.
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Question 4
4.
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Question 5
5.
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Question 6
6.
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Question 7
7.
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Question 8
8.
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Question 9
9.
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Question 10
10.
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Question 11
11.
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Question 12
12.
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Question 13
13.
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Question 14
14.
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You must show work for the following questions.
Question 15
15.
Write an equation that defines m(x) as a trinomial where m(x) = (3x - 1)(3 - x) + 4x
2
+ 19.
Solve for x when m(x) = 0. Work must be shown below to support your answer.
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Question 16
16.
In the equation x
2
+ 10x + 24 = (x + a)(x + b), b is an integer. Find algebraically all possible values of b.
Use the work area below if needed.
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Question 17
17.
Solve x
2
- 8x - 9 = 0 algebraically. Explain the first step you used to solve the given equation. You may write your in the work space below.
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Question 18
18.
Solve 5x
2
= 180 agebraically.
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Question 19
19.
If the zeros of a quadratic function F, are 2 and -6, what is the equation of the axis of symmetry of F ? Show all work below to justify your answer.
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Question 20
20.
Determine algebraically the zeros of f(x) = 3x
3
+ 21x
2
+ 36x. Show all work below. Write your answer in the blank using { }
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Question 21
21.
Please upload pictures of your work if you didn't use the space provided.
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Question 22
22.
Please upload pictures of your work if you didn't use the space provided.
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Question 23
23.
Please upload pictures of your work if you didn't use the space provided.
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Question 24
24.
Please upload pictures of your work if you didn't use the space provided.
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If 4x
2
- 100 = 0 , the roots of the equation are
-25 and 25
-25 only
-5 and 5
-5 only
Which equation is equivalent to y - 34 = x(x - 12) ?
y = (x - 17)(x + 2)
y = (x - 17)(x - 2)
y = (x - 6)
2
+ 2
y = (x - 6)
2
- 2
Which value of x is a solution to the equation 13 - 36x
2
= -12 ?
What is the solution set of the equation (x - 2)(x - a) = 0 ?
-2 and a
-2 and -a
2 and a
2 and -a
How many real-number solutions does 4x
2
+ 2x + 5 = 0 have ?
one
two
zero
infinitely many
Keith determines the zeros of the function f(x) to be -6 and 5. What could be Keith's function?
f(x) = (x + 5)(x + 6)
f(x) = (x + 5)(x - 6)
f(x) = (x - 5)(x + 6)
f(x) = (x - 5)(x - 6)
I only
II only
I and II
II and III
The graphs below represent functions defined by polynomials. For which function are the zeros of the polynomials 2 and −3?
1
2
3
4
A only
B only
A and C only
A, B, and C
Which polynomial function has zeros at -3, 0, and 4 ?
f(x) = (x + 3)(x
2
+ 4)
f(x) = (x
2
- 3)(x - 4)
f(x) = x(x + 3)(x - 4)
f(x) = x(x - 3)(x + 4)
For which function defined by a polynomial are the zeros of the polynomial -4 and -6 ?
The zeros of the function f(x) = 3x
2
- 3x - 6 are
-1 and -2
1 and -2
1 and 2
-1 and 2
1
2
3
4