Possible Rational Zeros List all possible rational zeros given by the Rational Zeros Theorem (bu

step 1 So now we are going to find the possible rational zeros of this polynomial right here. So again,

Possible Rational Zeros List all possible rational zeros...

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Key Concepts

Polynomial

A polynomial is an expression consisting of variables and coefficients combined using addition, subtraction, and multiplication with nonnegative integer exponents. Understanding the structure of a polynomial is essential for analyzing its behavior, including determining its zeros or roots.

Rational Zeros Theorem

The Rational Zeros Theorem provides a method for finding all possible rational zeros of a polynomial with integer coefficients. According to the theorem, any rational zero can be expressed in the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. This theorem narrows down the candidates that need to be tested to identify the actual zeros of the polynomial.

Factors of Constant Term and Leading Coefficient

Identifying the factors of the constant term and the leading coefficient is a crucial step in applying the Rational Zeros Theorem. The factors of the constant term represent the potential numerators (p values) and the factors of the leading coefficient represent the potential denominators (q values). By considering all combinations of these factors, one generates a complete list of possible rational zeros.

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