MATH Integrated Math III  - Unit 26: Remainder and Factor Theorems
For the first four problems, evaluate the polynomial expression for the indicated value of “x”.

1) Evaluate for x = –2.

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2) Evaluate for x = –1.

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3) Evaluate for x = 5.

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4) Evaluate for x = 3.

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For the next four problems, use these polynomials to select the simplified form for the given sum or difference. State the letter of the correct answer. Note: You will not use all answer choices.

5) Find the sum.

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6) Find the difference.

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7) Find the sum.

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8) Find the difference.

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For the next two questions, write “yes” or “no” for the problem denoting whether the linear expression is a factor of the polynomial.

9) Is the linear expression a factor of the polynomial?

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10) Is the linear expression a factor of the polynomial?

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For the next three problems, divide by using long division and determine if the given solution is true or false. If false, state the correct solution.

11) True or False? If false, state the correct solution.

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12) True or False? If false, state the correct solution.

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13) True or False? If false, state the correct solution.

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For the next three problems, divide using synthetic division and determine if the given solution is true or false. If false, state the correct solution.

14) True or False? If false, state the correct solution.

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15) True or False? If false, state the correct solution.

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16) True or False? If false, state the correct solution.

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For the next four problems, use factoring to find the “real” roots for the given polynomial equation.

17) Solve for “x”.

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18) Solve for “x”.

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19) Solve for “x”.

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20) Solve for “x”.

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For the next two problems, use a graph, synthetic division, and factoring to find all roots of the equation.

21) Solve for “x”.

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22) Solve for “x”.

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For the next two problems, use variable substitution and factoring to find all of the roots of the equation. State the letter of the correct answer.

23) Solve for “x”.

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24) Solve for “x”.

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For the next two problems, find all of the rational roots of the polynomial equation.

25) Solve for “x”.

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26) Solve for “x”.

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