Download Polynomial Review {L-1 to L-4}

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Algebra 2 Polynomial Review Sections 1-4
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Classify –2x4 – x3 + 8x2 + 12 by degree.
a. quartic
b. quintic
c.
d.
quadratic
cubic
2. Classify 8x4 + 7x3 + 5x2 + 8 by number of terms.
a. trinomial
c.
b. binomial
d.
polynomial of 5 terms
polynomial of 4 terms
3. Write –2x2(–5x2 + 4x3) in standard form.
a. –8x5 – 20x4
b. –8x5 + 10x4
–7x + 2x4
–7x5 – 10x4
c.
d.
Consider the leading term of each polynomial function. What is the end behavior of the graph?
4. −3x 3 − x
a. The leading term is −3x 3 .
down.
b. The leading term is −3x 3 .
up.
c. The leading term is −3x 3 .
up and down.
d. The leading term is −3x 3 .
down and up.
5. 5x 8 − 2x 7 − 8x 6 + 1
a. The leading term is 5x 8 .
down and up.
b. The leading term is 5x 8 .
down.
c. The leading term is 5x 8 .
d. The leading term is 5x 8 .
down.
Since n is odd and a is negative, the end behavior is down and
Since n is odd and a is negative, the end behavior is up and
Since n is odd and a is negative, the end behavior is
Since n is odd and a is negative, the end behavior is
Since n is even and a is positive, the end behavior is
Since n is even and a is positive, the end behavior is up and
Since n is even and a is positive, the end behavior is up and up.
Since n is even and a is positive, the end behavior is down and
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6. What is the graph of y =
1 3
x
4
a.
c.
b.
d.
Write the polynomial in factored form.
7. 6x3 – 60x2 + 144x
a. 6x(x – 6)(x + 4)
b. –4x(x – 6)(x + 6)
c.
d.
–6x(x + 6)(x – 4)
6x(x – 4)(x – 6)
8. x3 + 2x2 – 15x
a. 5x(x + 1)(x – 3)
b. x(x – 3)(x + 5)
c.
d.
x(x + 5)(x + 3)
–3x(x + 5)(x + 1)
9. What is a cubic polynomial function in standard form with zeros –4, –5, and 4?
a.
b.
f(x) = x 3 − 5x 2 − 16x + 20
f(x) = x 3 − 5x 2 + 16x − 80
c.
d.
f(x) = x 3 − 5x 2 + 11x − 80
f(x) = x 3 + 5x 2 − 16x − 80
2
What are the zeros of the function? What are their multiplicities?
10. f(x) = 4x 3 − 12x 2 − 16x
a. the numbers 1, –4, and 0 are zeros of multiplicity 2
b. the numbers –1, 4, and 0 are zeros of multiplicity 2
c. the numbers –1, 4, and 0 are zeros of multiplicity 1
d. the numbers 1, –4, and 0 are zeros of multiplicity 1
What are the zeros of the function? Graph the function.
11. y = x(x − 2)(x + 5)
a. 2, –5
b.
0, –2, 5
c.
0, 2, –5
d.
2, –5, –2
3
12. y = (x + 3)(x − 3)(x − 4)
a. 3, –3, –4
b.
–3, 3, 4
c.
3, –3, 4
d.
–3, 3, –4
What are the real or imaginary solutions of each polynomial equation?
13. 125x 3 + 343 = 0
a.
7 7
− ,
5 5
c.
7 35 ± 35i 3
− ,
5
50
b.
7 35 ± 35 3
,
5
50
d.
no solution
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What are the real or imaginary solutions of the polynomial equation?
14. x 3 − 8 = 0
a. 1 + i 3 and 1 − i
b.
3
2, −1 + i 3 , and −1 − i 3
15. x 3 = 216
a. −6, 3 + 3i
b. −6, 3 + 3i
7 , and 3 − 3i 7
3 , and 3 − 3i 3
d.
3 , and 1 − 2i 3
2, 2 + 2i 3 , and 2 − 2i 3
c.
6, 3 + 3i
c.
d.
2, 1 + 2i
7 , and 3 − 3i 7
6, −3 + 3i 3 , and −3 − 3i 3
Find the real solutions of the equation by graphing.
16. x 2 + 2x + 2 = 0
a.
c.
no solution
x=0
d.
b.
x=4
x=2
5
17. 6x = 9 + x 2
a.
c.
–3, 3
3
b.
d.
–3
no solution
18. Divide 4x 3 + 2x 2 + 3x + 4 by x + 4.
a. 4x 2 − 14x + 59
b. 4x 2 + 18x − 53, R 240
c.
d.
4x 2 − 14x + 59, R –232
4x 2 + 18x − 53
19. Divide −3x 3 − 2x 2 − x − 2 by x – 2.
a. −3x 2 + 4x + 15, R 32
b. −3x 2 + 4x + 15
c.
d.
−3x 2 − 8x − 17
−3x 2 − 8x − 17, R –36
20. Divide x 3 + x 2 − x + 2 by x + 4.
a. x 2 − 3x + 11, R –42
b. x 2 − 3x + 11
c.
d.
x 2 + 5x − 13
x 2 + 5x − 13, R 46
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