MATH Integrated Math III  - Unit 25: Solving Polynomial Equations
For the first five problems, use factoring to solve the equation.

1) Solve for “x”.

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2) Solve for “y”.

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3) Solve for “x”.

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4) Solve for “y”.

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5) Solve for “x”.

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For the next five problems, use a graph, synthetic division, and factoring to find all of the roots of the equation. State each root and its multiplicity.

6) Solve for “x”.

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7) Solve for “x”.

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8) Solve for “x”.

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9) Solve for “x”.

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10) Solve for “x”.

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For the next five problems, use variable substitution and factoring to find all of the roots of the equation. State the answer or the letter of the correct answer, whichever is appropriate.

11) Solve for “x”.

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12) Solve for “x”.

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13) Solve for “x”.

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14) Solve for “x”.

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15) Solve for “x”.

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For the next three problems, use the Rational Root Theorem to find all of the rational roots of each polynomial equation.

16) Solve for “x”.

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17) Solve for “x”.

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18) Solve for “x”.

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Short Answer

19) Explain how to use variable substitution to find all of the roots of the given polynomial, and then state the roots.

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20) When P(x) touches but does not cross the x-axis at (r, 0), what must be true of P(x)? Give an example of a polynomial for which this is true.

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