Finding Zeros of Polynomials

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What are the zeros of a polynomial?

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The zeros of a polynomial are the values of x that make the polynomial equal to zero. They are also known as the roots of the polynomial.

Tags

CCSS.HSF-IF.C.7C

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How do you find the zeros of a polynomial?

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To find the zeros of a polynomial, set the polynomial equal to zero and solve for x using factoring, the quadratic formula, or numerical methods.

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What is the Rational Root Theorem?

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The Rational Root Theorem states that any rational solution (or root) of a polynomial equation can be expressed as a fraction p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Tags

CCSS.HSA.APR.B.2

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (x) raised to whole number powers and coefficients, combined using addition, subtraction, and multiplication.

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What is a factor of a polynomial?

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A factor of a polynomial is a polynomial of lower degree that divides the original polynomial without leaving a remainder.

Tags

CCSS.HSA.APR.B.2

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What does it mean for a polynomial to have multiple roots?

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A polynomial has multiple roots when a particular root occurs more than once. For example, in (x-2)², the root x=2 is a double root.

Tags

CCSS.HSF-IF.C.7C

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial. For example, in 2x^3 + 3x^2 + 1, the degree is 3.

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How many roots can a polynomial have?

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A polynomial of degree n can have at most n roots, counting multiplicities.

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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 - c). It is faster than long division.

Tags

CCSS.HSA.APR.D.6

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What is the significance of the leading coefficient?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It affects the end behavior of the polynomial's graph.