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The rational root theorem is a method to find the rational solutions of a polynomial equation or function. It states that each rational zero of a polynomial with integer coefficients is of the form p/q, where p and q are relatively prime numbers. Learn how to use the theorem with proof, examples, and applications.
Learn how to find rational zeros of polynomial functions with integer coefficients using the rational zero theorem. See examples, definitions, and synthetic division methods.
The Rational Zero Theorem states that if a polynomial function has integer coefficients, then every rational zero of it has the form of a factor of the constant term and a factor of the leading coefficient. Learn how to apply this theorem with examples and exercises on College Algebra.
The rational root theorem is a tool to find all possible rational roots of a polynomial equation of the order 3 and above. It says that the roots are one of the combinations of the factors of the constant-coefficient and the factors of the nth coefficient. Learn how to use it with guided examples, test style practice questions, and the integral root theorem.
Learn how to use the Rational Zeros Theorem to find all the rational zeros of a polynomial with integer coefficients and a zero of the function. Follow the steps to arrange the polynomial in descending order, write down the factors of the constant and leading coefficient, and use synthetic division to simplify and cross out the factors.
In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational solutions of a polynomial equation a n x n + a n − 1 x n − 1 + ⋯ + a 0 = 0 {\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots +a_{0}=0}
The Rational Roots Test (or Rational Zeroes Theorem) is a handy way of obtaining a list of useful first guesses when you are trying to find the zeroes (or roots) of a polynomial.
