Solving Polynomial Equations

This worksheet focuses on solving polynomial equations of various degrees, including factoring, synthetic division, and the Rational Root Theorem for Grade 10 students.

Grade 10 Math AlgebraSolving Polynomial Equations

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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

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

Topics

AlgebraPolynomialsEquationsFactoringRational Root Theorem

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. Show all your work for full credit.

1. Solve the equation by factoring: x³ - 4x² + 3x = 0

2. Solve the equation by factoring: 2x⁴ - 16x = 0

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

4. Use synthetic division to determine if (x - 2) is a factor of P(x) = x³ - 5x² + 7x - 2. What is the remainder?

5. Given that x = -1 is a root of P(x) = x³ + 4x² + x - 2, use synthetic division to find the other roots.

6. Which of the following is a root of the polynomial P(x) = x³ - 6x² + 11x - 6?

x = -1

x = 0

x = 1

x = 6

7. If (x + 3) is a factor of a polynomial P(x), what is the value of P(-3)?

-3

Cannot be determined

8. A polynomial of degree 'n' can have at most 'n' real roots.

True

False