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Mathematics
11th -
12thgrade
Zeros and their Multiplicities of Polynomials
26 questions
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- 1. Multiple Choice
f(x)=(x+4)(x-3)(x-2)
List the zeros for this function.
x = -4, x = 3, x = -2
x = -4, x = 3, x = 2
x = -4, x = -3, x = 2
x = 4, x = 3, x = 2
- 2. Multiple Choice
Use the graph of f(x) to find the real solutions of f(x)=0.
0, 5
-2
0, -4
no real solution
- 3. Multiple ChoiceAll imaginary roots comes in pairs.TrueFalse
- 4. Multiple ChoiceUse the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root.-3+5i-3-5i-5i3-5i
- 5. Multiple ChoiceWhat is the complex conjugate of 4-3i?A. 1/(4-3i)B. 1/(4+3i)C. -4 + 3iD. 4 + 3i
- 6. Multiple Choice
Which of these is not an irrational number?
Square root of 13
Square root of 48
Square root of 9
Square root of 11
- 7. Multiple Choice
Is (x-8) a factor of (x2-16x+64)?
*you may graph or use synthetic division
Yes
No
- 8. Multiple Choice
If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?
Even
Odd
None
- 9. Multiple Choice
If the there is a turning point on the x-axis, what does that mean about the multiplicity of that zero?
Even
Odd
None
- 10. Multiple ChoiceClassify the function:quadraticcubicquarticlinear
- 11. Multiple ChoiceWhat are the roots of the polynomial function?
y = (x + 2)(x - 7)3-2, 7 multiplicity 3-2, 7, 32, -7 multiplicity 32, -7, 3 - 12. Multiple ChoiceOdd Multiplicities have which of the following effects on the x-axis?Cross the x-axisTurn on the x-axis
- 13. Multiple Choice
What are the zeros of the function?
3 , 1, 2 , 6
3, 1 , -2 , -5.2
-3, -1 , 2 , 5.2
-2 , 4 , 1 , 3
- 14. Multiple Choice
Even Multiplicities have which of the following effects on the x-axis?
touches and bounces back
wiggle
crosses the x-axis
- 15. Multiple ChoiceWhich zero has an odd multiplicity?-442-2
- 16. Multiple ChoiceWhich root has even multiplicity?1-4-12
- 17. Multiple ChoiceWhat is the equation in factored form of this graph?f(x) = (x-4)(x-1)2(x+2)(x+4)f(x) = (x-4)(x+1)2(x+2)(x+4)f(x) = (x-4)(x-1)2(x-2)(x+4)f(x) = (x+4)(x+1)2(x-2)(x-4)
- 18. Multiple ChoiceWhat could be the function for this graph in factored form?f(x) = (x-4)2(x+2)f(x) = (x+4)2(x-2)f(x) = (x-4)(x+2)2f(x) = (x+4)(x-2)2
- 19. Multiple ChoiceWhat is the Degree of this polynomial:
f(x)= x3(x + 3)2(x – 5)Degree: 6Degree: 5Degree: 3Degree: 2 - 20. Multiple ChoiceThe end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficientLeading Coefficient Positive
Degree - EvenLeading Coefficient Positive
Degree - OddLeading Coefficient Negative
Degree - EvenLeading Coefficient Negative
Degree - Odd - 21. Multiple Choice
Use the Quadratic Formula to solve for x:
x = {-3+2i , -3-2i}
x = {7, 6}
x = 2 ± i√3
No solution
- 22. Multiple ChoiceMultiply: (2 + 3i)(2 - 3i)4 - 9i134 + 6i + 9i213 + 6i
- 23. Multiple ChoiceHow many real zeros does the polynomial function below have? Hint: must look at graph.
P(x) = x3 + 2x2 + 9x + 180123 - 24. Multiple Choice
When given the FACTOR, what number do you divide by when using synthetic division? Example: (x + 5)
The number exactly
The opposite of the number
The number divided by itself
Zero
- 25. Multiple ChoiceWhat should be the order of the polynomial coefficients if
(3x - 4x3 + 6x4 + 1) / (x + 3)3 0 -4 6 16 -4 3 1 06 -4 0 3 1-6 4 0 -3 -1 - 26. Multiple Choice
What does this tell me?
f(-2)= -27 is a point on the graph
-2 is a solution of the function
(x+2) is a factor of the function
(x-2) is a factor of the function
- Answer choicesTagsAnswer choicesTags