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GEM T2 C3S4-5 RRT Solving Polynomial Equations
Presentation
•
Mathematics
•
10th Grade
•
Practice Problem
•
Easy
Gerard Crisologo
Used 1+ times
FREE Resource
25 Slides • 27 Questions
1
2
3
Multiple Choice
Which of the following best describes the significance of the Rational Root Theorem in algebra?
It helps identify all possible rational roots of a polynomial equation.
It guarantees that every polynomial has a rational root.
It is used to factor quadratic equations only.
It determines the degree of a polynomial.
4
Open Ended
Why is it important to determine the possible roots of a polynomial equation before attempting to solve it?
5
6
Multiple Choice
According to the Fundamental Theorem of Algebra, how many roots does a polynomial equation of degree n have, counting multiplicity?
n
n+1
n-1
2n
7
8
Multiple Select
Which of the following are valid methods for solving quadratic equations?
Factoring
Completing the square
Using the quadratic formula
Synthetic division
9
Open Ended
Explain the difference between solving incomplete and complete quadratic equations. Provide an example for each type.
10
Multiple Choice
What are the roots of the equation x^3 + 6x^2 - 4x - 24 = 0?
1, -1, 2
2, -2, -6
3, -3, 6
4, -4, 5
11
12
13
Multiple Choice
If a rational number L/F is a root of a polynomial equation with integer coefficients, what must be true about L and F?
L is a factor of the constant term and F is a factor of the leading coefficient
L is a factor of the leading coefficient and F is a factor of the constant term
L and F must both be prime numbers
L and F must both be negative
14
15
Fill in the Blanks
Fill in the blank: In the Rational Root Theorem, possible rational roots are given by the factors of the
16
17
Multiple Choice
What are the possible rational roots of the equation x^3 + 6x^2 + 11x + 6 = 0 according to the Rational Root Theorem?
1, -1, 2, -2, 3, -3, 6, -6
1, 2, 3, 6
-1, -2, -3, -6
0, 1, -1, 2
18
19
Open Ended
According to the Fundamental Theorem of Algebra, how many roots does the equation x^3 + 6x^2 + 11x + 6 = 0 have, and what methods can be used to find them?
20
21
Fill in the Blanks
The expression obtained after dividing x^3 + 6x^2 + 11x + 6 by (x + 1) is x^2 +
22
23
Open Ended
Explain how synthetic division is used to find the roots of a cubic polynomial, using x^3 + 6x^2 + 11x + 6 as an example.
24
25
Multiple Select
Which of the following are roots of the equation x^3 + 6x^2 + 11x + 6 = 0?
-1
-2
-3
1
26
27
Multiple Choice
What are the possible rational roots of the equation x^3 - 3x^2 - 33x + 35 = 0 as determined by the Rational Root Theorem?
1, -1, 5, -5, 7, -7, 35, -35
1, -1, 2, -2, 3, -3, 6, -6
1, 5, 7, 35
-1, -5, -7, -35
28
29
Multiple Choice
Which of the following are possible rational roots for the equation x^3 - 3x^2 - 33x + 35 = 0 according to the Rational Root Theorem?
1, -1, 5, -5, 7, -7, 35, -35
2, -2, 10, -10, 14, -14, 70, -70
1, 2, 3, 4, 5, 6, 7, 8
0, 1, -1, 2, -2, 3, -3, 4
30
31
Open Ended
Describe the process of using synthetic division to test possible roots for a cubic polynomial equation.
32
33
Multiple Choice
Which of the following are the roots of the equation x^3 - 3x^2 - 33x + 35 = 0?
1, -5, 7
1, -1, 5
-1, 5, 7
-5, 7, 35
34
35
Fill in the Blanks
After using synthetic division on x^3 - 3x^2 - 33x + 35, the resulting quadratic equation is x^2 -
36
37
Multiple Choice
What are the possible rational roots for the equation x^3 - 11x^2 - x + 11 = 0 according to the Rational Root Theorem?
1, -1, 11, -11
1, -1, 5, -5
1, 2, 11, 22
1, -1, 7, -7
38
39
40
Multiple Choice
Which of the following is NOT a possible rational root of the equation 2x^4 + x^3 - 8x^2 - x + 6 = 0 based on the Rational Root Theorem?
±1
±2
±3
±4
41
42
Multiple Select
Which of the following are roots of the polynomial 2x^4 + x^3 - 8x^2 - x + 6 = 0?
-2
1
-1
2
43
Open Ended
Explain the process of using synthetic division to find the roots of a polynomial equation, using the example 2x^4 + x^3 - 8x^2 - x + 6 = 0.
44
45
Fill in the Blanks
Fill in the blank: The remainder is
46
47
Open Ended
For how many positive integers n is n^3 - 8n^2 + 20n - 13 a prime number?
48
49
Multiple Select
Which of the following methods can be used to solve for the actual roots of a polynomial as mentioned in the synthesis slide?
Synthetic division
Quadratic formula
Completing the square
Factoring
50
51
Open Ended
Reflecting on today’s lesson, what questions do you still have about the Rational Root Theorem or solving polynomial equations?
52
Multiple Choice
How can the Rational Root Theorem help you solve polynomial equations?
It helps identify possible rational roots to test for solutions.
It provides the exact roots of any polynomial equation.
It only works for quadratic equations.
It is used to factor trinomials only.
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