Use Rational Root Theorem to find the Zeros of the Polynomial

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What is the Rational Root Theorem?

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The Rational Root Theorem states that if a polynomial has rational roots, they can be expressed as the ratio of factors of the constant term and the leading coefficient.

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How do you apply the Rational Root Theorem to find possible rational roots?

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List all factors of the constant term and the leading coefficient, then form all possible fractions of these factors.

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What is a zero of a polynomial?

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A zero of a polynomial is a value of x that makes the polynomial equal to zero.

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If (x - r) is a factor of a polynomial, what does it imply about r?

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If (x - r) is a factor, then r is a zero of the polynomial.

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

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Substitute the number into the polynomial. If the result is zero, then it is a zero.

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What is synthetic division?

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Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form (x - r).

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What is the significance of finding all zeros of a polynomial?

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Finding all zeros helps in understanding the behavior of the polynomial function, including its graph and intercepts.

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

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A polynomial of degree n can have up to n real zeros.

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How do you factor a polynomial given one of its zeros?

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Use synthetic division to divide the polynomial by (x - r), where r is the known zero, to find the remaining factors.

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What is the role of the constant term in the Rational Root Theorem?

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The constant term helps identify possible rational roots by providing its factors.