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 roots.

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How can you find the zeros of a polynomial?

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You can find the zeros of a polynomial by factoring the polynomial, using the quadratic formula, or graphing the polynomial to identify where it crosses the x-axis.

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What is the Rational Root Theorem?

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The Rational Root Theorem states that any rational solution (or zero) of a polynomial equation is of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

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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 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.

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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 2x³ + 3x² - x + 5, the degree is 3.

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How do you determine the number of zeros a polynomial can have?

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The Fundamental Theorem of Algebra states that a polynomial of degree n can have up to n zeros, 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.

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What is Desmos Graphing Calculator used for?

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Desmos Graphing Calculator is an online tool used to graph functions, analyze their behavior, and find zeros visually.

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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.