Chapter+2

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=Chapter 2 - Polynomial Functions =  media type="custom" key="3943001" media type="custom" key="3943029"

Section 2-1
Polynomials - If there is an (x) in the denominator, it is not a polynomial function. - Zero's or roots come from the numerator. Ex: x+3 || media type="custom" key="3943015"
 * __2x³-18x__
 * 2x³-18x=0 ||
 * 2x(x²-9)=0 ||
 * 2x(x+3)(x-3)=0 ||
 * Zeros: -3, 3, 0 Undefined: -3 ||



Section 2-2
- Synthetic Division; The Remainder and Factor Theorems

When polynomial P(x) is divided by x-a, the remainder is P(a).

For a polynomial P(x), x-a is factor if only if P(a) = 0.

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Section 2-3
Graphing Polynomial Functions

Graph of f(x) = ax³ + bx² + cx + d is usually shaped like a "sideways S." Graph of f(x) = ax⁴ + bx³ + cx² + dx + e shaped like a curvy "M" or "W."



Section 2-4
Finding Maximums and Minimums of Polynomial Functions Maximum or mimimum value of f(x) = ax² + bx + c occurs at -b/2a

Local Maximum or Local Minimum occurs at the "peak" or "valley" of a cubic function.



Section 2-5
Using Technology to Approximate Roots of Polynomial Equations

If P(x) is a polynomial with real coefficients and a and b are real numbers such that P(a) and P(b) have opposite signs, then between a and b there is at least one real root r of the equation P(x).



Section 2-6
Solving Polynomial Equations by Factoring



Section 2-7
General Results for Polynomial Equations

Theorom 1. The Fundamental Theorom of Algebra In the complex number system consisting of al rea and imaginary numbers, if P(x) is a polynomial of degree n (n>0) with cimplex coefficients, then the equation P(x) =0 has exactly n roots (provided a double root is counted as 2 roots, a triple root is counted as 3 roots, and so on).

Theorom 2. Complex Conjugates Theorom If P(x) is a polynomial with real coefficients, and a+bi is an imaginary root of the equation P(x) =0, then a-bi is also a root.

Theorom 3. Suppose P(x) is a polynomial with rational coefficients, and a and b are rational numbers such that the square root of b is irrational. If a + the square root of b is a root of the equation P(x) = 0, then a - the square root of b is also a root.

Theorom 4. If P(x) is a polynomial of odd degree with real coefficients, then the equation P(x) = 0 has at least one real root.