Solving Polynomial Equations Worksheet

Grade 11 Math worksheet focusing on solving polynomial equations, including factoring, rational root theorem, and synthetic division.

Grade 11 Math AlgebraSolving Polynomial Equations

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2 Short AnswerFill in the BlanksMultiple ChoiceLong Answer

Standards

CCSS.MATH.CONTENT.HSA.APR.B.2CCSS.MATH.CONTENT.HSA.APR.B.3CCSS.MATH.CONTENT.HSA.SSE.A.2

Topics

AlgebraPolynomialsEquationsFactoringRational Root TheoremSynthetic Division

7 sections · Free to use · Printable

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Solving Polynomial Equations

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Read each question carefully and solve the polynomial equations using the most appropriate method. Show all your work for full credit.

1. Solve the following polynomial equation by factoring: x³ - 4x² + 4x = 0

2. Find all real solutions for the equation: x⁴ - 16 = 0

3. According to the Rational Root Theorem, the possible rational roots of the polynomial P(x) = 2x³ + 3x² - 8x + 3 are .

4. If (x - 1) is a factor of the polynomial P(x) = x³ - kx² + 3x - 1, then the value of k must be .

5. Use synthetic division to find the quotient and remainder when P(x) = x³ + 2x² - 5x - 6 is divided by (x + 1).

6. Given that x = 2 is a root of the polynomial equation x³ - 7x + 6 = 0, find the other roots.

7. Which of the following is a possible rational root of P(x) = 3x³ - 5x² + 4x - 2?

1/3

2/5

3/2

8. How many real roots does the polynomial x⁴ + 5x² + 6 = 0 have?

9. Find all roots (real and complex) of the polynomial equation: x⁴ - 5x³ + 7x² - 5x + 6 = 0. You may use any method you deem appropriate, but show all steps clearly.