Rational Root Theorem Worksheet

A Grade 11 Math worksheet focusing on applying the Rational Root Theorem to find possible rational roots of polynomial equations.

Grade 11 Math AlgebraRational Root Theorem

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Includes

Fill in the Blanks2 Short AnswerMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSA.APR.C.2CCSS.MATH.CONTENT.HSA.APR.C.4

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Rational Root Theorem

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Read each question carefully and show all your work. Use the Rational Root Theorem to find all possible rational roots for the given polynomial equations.

1. According to the Rational Root Theorem, if a polynomial has integer coefficients, then every rational root of the polynomial must be of the form p/q, where p is a factor of the and q is a factor of the .

2. For the polynomial P(x) = ax^n + ... + cx + d, the possible rational roots are found by dividing factors of the (d) by factors of the (a).

3. List all possible rational roots for the polynomial P(x) = 2x^3 + 3x^2 - 8x + 3.

4. Determine all possible rational roots for the polynomial P(x) = x^4 - 5x^3 + 2x^2 + 20x - 24.

5. Which of the following is NOT a possible rational root for the polynomial P(x) = 3x^3 - 4x^2 - 5x + 2?

-2

1/3

3/2

6. For the polynomial P(x) = 6x^3 + 7x^2 - x - 2, which of the following is a possible rational root?

1/4

-2/3

5/6

7. The Rational Root Theorem guarantees that a polynomial will have at least one rational root.

True

False

8. If a polynomial has a leading coefficient of 1, then any rational root must be an integer.

True

False

9. Find all rational roots of the equation x^3 - 7x - 6 = 0.

10. Find all rational roots of the equation 2x^3 - 5x^2 - 4x + 3 = 0.