Rational zero theorem (Polynomial functions)

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What is the Rational Zero Theorem?

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The Rational Zero Theorem states that if a polynomial has rational roots, they can be expressed as the ratio of factors of the constant term (p) to factors of the leading coefficient (q).

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What does 'p' represent in the Rational Zero Theorem?

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In the Rational Zero Theorem, 'p' represents the factors of the constant term of the polynomial.

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What does 'q' represent in the Rational Zero Theorem?

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In the Rational Zero Theorem, 'q' represents the factors of the leading coefficient of the polynomial.

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How do you determine the possible rational zeros of a polynomial?

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To determine possible rational zeros, list all factors of the constant term (p) and all factors of the leading coefficient (q), then form all possible fractions p/q.

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What is synthetic division?

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Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor of the form (x - c).

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How can you verify if a number is a root of a polynomial?

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To verify if a number is a root, substitute it into the polynomial. If the result is zero, then it is a root.

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What is the maximum number of real zeros a polynomial can have?

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The maximum number of real zeros a polynomial can have is equal to its degree.

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What is the significance of the leading coefficient in a polynomial?

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The leading coefficient determines the end behavior of the polynomial function and influences the shape of its graph.

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How do you find the remaining factors of a polynomial after using synthetic division?

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After synthetic division, the quotient polynomial can be factored further to find the remaining factors.

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What is the relationship between the degree of a polynomial and its zeros?

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The degree of a polynomial indicates the maximum number of zeros (real and complex) it can have.