Rational Root Theorem Worksheet

Grade 12 Math worksheet on the Rational Root Theorem, including identifying possible rational roots and finding actual roots of polynomial functions.

Grade 12 Math AlgebraRational Root Theorem

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Includes

Fill in the BlanksMultiple Choice2 Short AnswerTrue / False

Standards

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

Topics

MathAlgebraRational Root TheoremPolynomialsGrade 12

7 sections · Free to use · Printable

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Rational Root Theorem

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Read each question carefully and answer to the best of your ability. Show all your work for full credit.

For each polynomial function, list all possible rational roots using the Rational Root Theorem.

1. f(x) = 2x³ + 3x² - 8x + 3 Possible rational roots:

2. g(x) = 4x⁴ - 7x³ + 2x - 5 Possible rational roots:

3. h(x) = x⁵ - 6x³ + 2x² + 12 Possible rational roots:

Which of the following is NOT a possible rational root for the polynomial P(x) = 3x³ - 5x² + 4x - 6?

1/3

3/2

Find all rational roots of the polynomial function f(x) = x³ - 4x² + x + 6.

Use the Rational Root Theorem and synthetic division to find all roots (real and complex) of the polynomial P(x) = 2x³ - 5x² - 4x + 3. Write the polynomial in factored form.

For a polynomial with integer coefficients, if p/q is a rational root, then p must be a factor of the constant term and q must be a factor of the leading coefficient.

True

False