Rational Root Theorem Worksheet
Practice applying the Rational Root Theorem to find possible rational roots of polynomial equations.
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Rational Root Theorem Practice
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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.
True
False
2. If p/q is a rational root of a polynomial, then P(p/q) = 0.
True
False
1. Which of the following is NOT a possible rational root of P(x) = 3x^3 - 4x^2 + 2x - 1?
1
-1/3
1/2
1/3
2. For the polynomial P(x) = 4x^4 - 5x^2 + 1, what are the factors of the constant term?
±1, ±2
±1
±1, ±4
±1, ±1/2, ±1/4
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.
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