PC - Sem 1 Units 2-3 Review Polynomial and Rational Functions

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What is a polynomial function?

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A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where n is a non-negative integer.

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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 expression. For example, in the polynomial 4x^3 + 3x^2 + 2, the degree is 3.

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What is a rational function?

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A rational function is a function that can be expressed as the quotient of two polynomials, in the form f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) ≠ 0.

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How do you find the vertical asymptote of a rational function?

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To find the vertical asymptote of a rational function f(x) = P(x)/Q(x), set the denominator Q(x) to zero and solve for x. The values of x that make Q(x) = 0 are the vertical asymptotes.

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What is the horizontal asymptote of a rational function?

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The horizontal asymptote of a rational function depends on the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If they are equal, it is y = a/b, where a and b are the leading coefficients.

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What does it mean to factor by grouping?

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Factoring by grouping is a method used to factor polynomials with four or more terms by grouping terms in pairs, factoring out the common factors, and then factoring the resulting expression.

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Solve for x: 2x^2 - 8 = 0.

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x = -2, x = 2.

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What is the remainder theorem?

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The remainder theorem states that if a polynomial f(x) is divided by (x - c), the remainder of that division is f(c).

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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 binomial of the form (x - c). It is faster than long division and involves using the coefficients of the polynomial.

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

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