Polynomial Functions Review

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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 a_n ≠ 0.

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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 equals zero. They are also known as the roots of the polynomial.

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How do you find the zeros of a polynomial function?

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

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What is the end behavior of polynomial functions?

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The end behavior of a polynomial function describes how the function behaves as x approaches positive or negative infinity. It is determined by the leading term of the polynomial.

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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. It indicates the polynomial's behavior and the number of possible zeros.

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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 divisor of the form (x - c). It is faster than long division and is used to find polynomial quotients and remainders.

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What is the Factor Theorem?

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The Factor Theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x). This helps in factoring polynomials.

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What is the Remainder Theorem?

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The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder is f(c). This can be used to evaluate polynomials quickly.

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Factor the polynomial: x^3 + 3x^2 - 4x - 12.

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(x + 3)(x + 2)(x - 2)

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Simplify the expression: (2x^3 - 5x^2 + 3x + 7) ÷ (x - 2).

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2x^2 - x + 1 + \frac{9}{x - 2}.