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SMIII Chapter 6 Review Worksheet
Name: ______________________________________
Pd: ______
Test Date: __________ Makeup :___________
Definitions
1. Average rate of change
2. Remainder Theorem
3. Factor Theorem
4. Rational Root Theorem
6.1
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8.
7.
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6.2
11. x - 6
12. 4x + 3
13. 9x- 18
14. -7
15. 8
16. 2/3
Hint: Use Long Division or Synthetic Division.
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Determine the quotient using polynomial long division. Write the dividend as the product of the (divisor) and (the
quotient plus the remainder.)
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Determine each quotient using synthetic division. Don’t forget to use placeholders, if necessary. Write the dividend as
the product of the (divisor) and (the quotient plus the remainder.)
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6.3 Determine each function value using the Remainder Theorem (use division). Explain your reasoning.
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Use the Factor Theorem to determine whether the given expression is a factor of each polynomial. Explain your
reasoning.
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Use the Factor Theorem to determine whether g(x) is the factored form of f(x).
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Use the Factor Theorem to determine the unknown coefficient so that the given linear expression is a factor of the
function.
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6.4 Factor each expression by factoring out the greatest common factor.
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Factor each expression completely using the reverse box method.
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6.5 Determine the possible rational roots of each polynomial using the Rational Root Theorem.
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Use the Rational Root Theorem to determine the possible rational roots for each polynomial equation. Then, SOLVE
COMPLETELY. (Be prepared to do this type of a problem without a graphing calculator.)
46. 𝑥 3 − 7𝑥 + 6
47. 2𝑥 3 + 8𝑥 2 − 14𝑥 − 20