POLYNOMIAL 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 f(x) = 4x^3 + 2x^2 + 5, the degree is 3.

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What is the leading coefficient of a polynomial?

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The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in f(x) = 3x^4 + 2x^3 + 1, the leading coefficient is 3.

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What does end behavior of a polynomial function refer to?

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End behavior describes how the values of a polynomial function behave as the input approaches positive or negative infinity. It is determined by the leading term of the polynomial.

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How do you find the roots of a polynomial equation?

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To find the roots of a polynomial equation, set the polynomial equal to zero and solve for the variable. This can be done using factoring, the quadratic formula, or numerical methods.

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What is the factored form of a polynomial?

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The factored form of a polynomial expresses it as a product of its factors. For example, f(x) = (x - 1)(x + 2) is a factored form of a polynomial.

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What is the quadratic formula?

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The quadratic formula is used to find the roots of a quadratic equation in the form ax^2 + bx + c = 0. It is given by: x = (-b ± √(b² - 4ac)) / (2a).

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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 and is used to find polynomial roots.

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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 the Factor Theorem?

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The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.