Rational Root Theorem Worksheet

Rational Root Theorem

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?

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.