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Name _______________________________________ Date __________________ Class __________________
Unit 2 Final Review
Polynomials
1. Rewrite the polynomial in standard form. Then identify the leading coefficient, degree,
and number of terms. Name/classify the polynomial.
x 2  3  2x 5  7x 4  12x
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2. Find h(x) – 4k(x) for h(x) = x2 – 8 and k(x) = 3x3 – 6x – 4 + 9x2
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3. Find the product: (x  2)(x 2  2x  12)
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4. Use the Binomial Theorem to expand the binomial: (2x  7)4
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5. Divide by using long division: (2x 3  10x 2  x  5)  (x  5)
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6. Divide by using synthetic division: (3x 2  8x  4)  (x  2)
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7. Write the expression that represents the length of a rectangle with
width x + 3 and area 5x2 – 4x + 12.
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8. Solve the polynomial equation by factoring: x 5  2x 4  24x 3  0
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Name _______________________________________ Date __________________ Class __________________
9. Use the graph of f(x) = x 4  2x 3  8x 2  0 to identify the values of x
for which f(x) = 0 and to factor f(x).
10. Identify the roots of the equation. State the multiplicity of each
root. x 3  5x 2  8x  48  0
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11. Solve the equation by finding all roots:
x 4  2x 3  14x 2  2x  15  0
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12. Factor: x 3  3x 2  9x  27  0
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13. Write the polynomial function that has zeros at 5 and 2 - i.
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14. Identify the leading coefficient, degree, and end behavior:
Q(x)  4x 3  x  1
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Name _______________________________________ Date __________________ Class __________________
15. Identify whether the function graphed has an odd or even degree
and a positive or negative leading coefficient.
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16. Graph the function P(x)  x 3  6x 2  5x  12.
17. Find the first 5 terms of the sequence: an  n2  2n
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18. Find the 8th term of the geometric sequence with the given terms:
a11  4 and a13  36
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Find the indicated sum for each geometric series.
19. S7 for 14, 42, 126, 378, 
8
20.
  4 
k 1
k 1
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