Semester Exam PreCalculus

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers and coefficients. For example, f(x) = 2x^3 + 3x^2 - 5 is a polynomial.

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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 for which the polynomial evaluates to zero. They are also known as the roots of the polynomial.

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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, in the form of p/q, is such that p is a factor of the constant term and q is a factor of the leading coefficient.

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How do you find the zeros of a polynomial?

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To find the zeros of a polynomial, you can use methods such as factoring, synthetic division, or applying the Rational Root Theorem, and then solving for x.

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What is synthetic division?

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

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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 the polynomial 4x^5 + 3x^2 - 2, the degree is 5.

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What is the leading coefficient of a polynomial?

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The leading coefficient of a polynomial is the coefficient of the term with the highest degree. For example, in 3x^4 + 2x^3 - x, the leading coefficient is 3.

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What is polynomial long division?

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Polynomial long division is a method used to divide a polynomial by another polynomial of equal or lower degree, similar to long division with numbers.

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What is the difference between a polynomial and a rational function?

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A polynomial is a sum of terms with non-negative integer exponents, while a rational function is a ratio of two polynomials.

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How do you determine if a number is a zero of a polynomial?

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To determine if a number c is a zero of a polynomial f(x), substitute c into the polynomial and check if f(c) = 0.