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SUPER
Mathematics
10th -
11thgrade
Remainder Theorem and Factor Theorem
20 questions
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- 1. Multiple Choice
Yes, x-3 is a factor of p(x) since the remainder is 0.
No, x-3 is not a factor of p(x) since the remainder is 0.
- 2. Multiple Choice
- 3. Multiple Choice
- 4. Match
Match the following appropriately.
It is important you can recognize the connection between factors and solutions.
x-1 is a factor of p(x).
1 is a solution of p(x).
x - 3 is a factor of p(x).
3 is a solution of p(x).
2x - 3 is a factor of p(x).
3/2 is a solution of p(x).
x is a factor of p(x).
0 is a solution of p(x).
- 5. Match
Match the following appropriately.
It is important you can recognize the connection between factors and solutions.
5 is a solution of p(x).
x + 3 is a factor of p(x).
-3 is a solution of p(x).
x - 5 is a factor of p(x).
-5 is a solution of p(x).
3x - 5 is a factor of p(x).
5/3 is a solution of p(x).
x + 5 is a factor of p(x).
- 6. Multiple Choice
1 is a solution of p(x)
1 is not a solution of p(x)
x -1 is a factor of p(x)
x+1 is not a factor of p(x)
- 7. Match
Match the following:
x + 2...
-2...
The remainder is...
0
The work provided shows the polynomial 5x2 - 10x - 40 being divided by...
x+2
- 8. Multiple Choice
x-7 is a factor of p(x).
x+7 is a factor of p(x).
-7 is a solution of p(x).
7 is a solution of p(x).
- 9. Multiple Choice
Which statement accurately describes what this work demonstrates?
- 10. Multiple Choice
5 is a solution of p(x) since the remainder is 0.
5 is a solution of p(x) since the remainder is 100.
5 is not a solution of p(x) since the remainder is 0.
5 is not a solution of p(x) since the remainder is 100.
- 11. Multiple Choice
x-5 is a factor of p(x) since 5 was a solution.
x-5 is not a factor of p(x) since 5 was not a solution.
x+5 is not a factor of p(x) since 5 was not a solution.
x+5 is a factor of p(x) since 5 was a solution.
- 12. Multiple Choice
- 13. Multiple Choice
True
False
- 14. Multiple Choice
Complete the synthetic division and use the remainder to determine a true statement concerning p(x) and its solutions.
-2 is a solution of p(x) since the remainder is equal to 0.
-2 is not a solution of p(x) since the remainder is equal to 1.
-2 is not a solution of p(x) since the remainder is equal to 33.
2 is not a solution of p(x) since the remainder is equal to -1.
- 15. Multiple Choice
Complete the rest of this synthetic division problem.
Determine the remainder.
The remainder is 18.
The remainder is 0.
The remainder is 108.
The remainder is 28.
- 16. Multiple Choice
Based on the remainder you found, which statement is true?
- 17. Multiple Choice
Based on the remainder you found, which statement is true?
- 18. Multiple Choice
Assume that a polynomial has a solution at the x-value 4.
Which of the following must be a factor of that same polynomial?
4x
x-4
x+4
- 19. Multiple Choice
Assume that x-2 is a factor of a polynomial. Which x-value must be a solution of that same polynomial?
The x-value -2
The x-value 2
The x-value 0
- 20. Multiple Choice
C would need to be equal to 0.
C would need to be equal to 12.
C would need to be equal to -12.
C would need to be equal to 300.
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