Rational Root Theorem Worksheet

Rational Root Theorem Practice

Read each question carefully and follow the instructions to find the possible rational roots of the given polynomial equations.

1. According to the Rational Root Theorem, if a polynomial has integer coefficients, then every rational root of the polynomial can be expressed in 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 + ... + bx + c, the possible rational roots are found by dividing factors of the   by factors of the  .

1. List all possible rational roots for the polynomial P(x) = x^3 - 2x^2 - 5x + 6.

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

1. All polynomial equations have at least one rational root.

2. If p/q is a rational root of a polynomial, then P(p/q) = 0.

1. Which of the following is NOT a possible rational root of P(x) = 3x^3 - 4x^2 + 2x - 1?

2. For the polynomial P(x) = 4x^4 - 5x^2 + 1, what are the factors of the constant term?

1. Find all rational roots of the polynomial P(x) = x^3 + 2x^2 - x - 2.

2. Using the Rational Root Theorem, find the rational roots of P(x) = x^4 - 5x^2 + 4.