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Polynomials and Polynomial Functions Unit Test
06/12/15 12:52
Polynomials and Polynomial Functions Unit Test
Frank Gjurashaj is taking this assessment.
1.
(1 point)
Which equation is most likely represented by the graph above?
y = (2x – 1)(2x – 3)(2x + 5)
y = (2x + 1)(2x + 3)(2x – 5)
y = –(2x + 1)(2x + 3)(2x – 5)
y = (2x + 1)(2x + 3)(2x + 5)
2.
(1 point)
What are the apparent zeros of the cubic function graphed above?
{–1}
{0, 2}
{–1, 2}
{–2, 1, 2}
3. What is a polynomial function in standard form with zeros 1, 2, –2, and –3? (1 point)
x4 + 2×3 + 7×2 – 8x + 12
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x4 + 2×3 – 7×2 – 8x + 12
x4 + 2×3 – 7×2 + 8x + 12
x4 + 2×3 + 7×2 + 8x + 12
4. What are the zeroes of the function? What are their multiplicities? (1 point)
f (x) = 4×3 – 20×2 + 24x
The numbers –3, –2, and 0 are zeroes of multiplicity 1.
The numbers 3, 2, and 0 are zeroes of multiplicity 2.
The numbers –3, –2, and 0 are zeroes of multiplicity 2.
The numbers 3, 2, and 0 are zeroes of multiplicity 1.
5. What are the real and complex solutions of the polynomial equation? (1 point)
x3 – 8 =0
1 + i , and 1 – i
2, –1 + i , and –1 – i
2, 1 + 2i , and 1 – 2i
2, 2 +2i , and 2 – 2i
6. Which is equivalent to the following expression? (1 point)
(2×2 + 4xy – y2) + (x2 + 3xy – y2)
3×2 – 7xy – 2y2
3×4 + 7xy – 2y4
3×2 + 7xy – 2y2
2×2 – 7xy + 2y2
7. Which is a factored form of 27×3 + 64? (1 point)
(3x + 4)(9×2 – 24x + 16)
(3x + 4)(9×2 + 24x + 16)
(3x + 4)(9×2 – 12x + 16)
(3x + 4)(9×2 + 12x + 16)
8. Divide –2×3 – 4×2 + 3x + 2 by x – 3. (1 point)
–2×2 – 10x – 27, R –79
–2×2 – 10x –27
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–2×2 – 10x – 27, R 83
–2×2 – 10x + 27, R 83
9. Find the roots of the polynomial equation. (1 point)
x3 – 4×2 + x + 26
3 + 2i, 3 – 2i, –2
3 + 2i, 3 – 2i, 2
–3 + 2i, –3 – 2i, 2
–3 + 2i, –3 – 2i, –2
10. Which correctly describes the roots of the following cubic equation? (1 point)
x3 – 5×2 + 3x + 9 = 0
Three real roots, each with a different value
One real root and two complex roots
Three real roots, two of which are equal in value
Two real roots and one complex root
11. What is the second term of (p + q)5? (1 point)
25p4
5p4q
25p4q
125p4q
12. One zero of f(x) = x3 – 6×2 + 11x – 6 is 3. What are other zeros of the function? (1 point)
1 and 3
–1 and –2
1 and 2
–1 and 3
13. Which of the following quartic functions has x = –1 and x = –3 as its only two real zeros? (1 point)
y = x4 – 4×3 – 4×2 – 4x – 3
y = –x4 + 4×3 + 4×2 + 4x + 3
y = x4 +4×3 + 3×2 + 4x – 4
y = x4 + 4×3 + 4×2 + 4x + 3
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Polynomials and Polynomial Functions Unit Test
14. Work Pad
06/12/15 12:52
(2 points)
Note: Remember to show all of the steps that you use to solve the problem. You can use the
comments field to explain your work. Your teacher will review each step of your responses to
questions 13–19 to ensure you receive proper credit for your answers.
The design of a digital box camera maximizes the volume while keeping the sum of the
dimensions at 6 inches. If the length must be 1.5 times the height, what should each dimension
be?
Hint: Let x represent one of the dimensions, and then define the other dimensions in terms of x.
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Polynomials and Polynomial Functions Unit Test
15.
What are the real and complex solutions of the polynomial equation?
06/12/15 12:52
(2 points)
x4 – 41×2 = –400
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16.
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Use synthetic division to find P(–3) for P(x) = x4 – 2×3 – 4x + 4. (2 points)
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17. Find all the zeroes of the equation. (2 points)
x4 – 6×2 – 7x – 6 = 0
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Polynomials and Polynomial Functions Unit Test
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18. Use Pascal’s triangle to expand the binomial. (2 points)
(d – 5y)6
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Polynomials and Polynomial Functions Unit Test
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19. What is the equation of = 3 with the given transformations?
y x
vertical compression by a factor of , horizontal shift 8 units to the left, reflection across the
(2 points)
x-axis
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20. What are all the real zeroes of = ( –12)3 – 7? (2 points)
y x
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Essay
Note: Your teacher will grade your response to ensure you receive proper credit for your answer.
21. Explain how to find the degree of a polynomial. (2 points)
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22. Can you always use synthetic division for dividing polynomials? Explain. (2 points)
23. If 2 +
is a polynomial root, name another root of the polynomial, and explain how you
know it must also be a root.
(2 points)
24. How can you quickly determine the number of roots a polynomial will have by looking at the
equation?
(2 points)
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Polynomials and Polynomial Functions Unit Test
25.
Is
a power function? Explain your reasoning.
06/12/15 12:52
(2 points)
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