8 polynomial functions

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8 polynomial functions

  1. 1. Polynomial Functions<br />Prepared by:<br />Prof. Teresita P. Liwanag-Zapanta<br />B.S.C.E, M.S.C.M., M.Ed Math (units), PhD-TM (on-going)<br />
  2. 2. SPECIFIC OBJECTIVES:<br />At the end of the lesson, the student is expected to be able to:<br /><ul><li>Identify a polynomial function.
  3. 3. Distinguish a polynomial function from among different types of functions.
  4. 4. Determine the degree of a polynomial function.
  5. 5. Determine the value of the function with the use of the Remainder Theorem.
  6. 6. Use the Factor Theorem to determine the factors of a polynomial.
  7. 7. Use Descartes’ Rule of Signs to determine the maximum number of positive and negative roots of a polynomial equation.
  8. 8. Locate all possible rational roots/zeroes of a polynomial equation.
  9. 9. Approximate the graph of a polynomial function.</li></li></ul><li> <br />
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  15. 15. Definition: The Roots/Zeroes of polynomials<br /> If f(r) = 0 , then r is a zero/root/ solution of the polynomial equation <br />That is, f(x) = (x-r) Q(x).<br />Remarks: <br />1. The Fundamental Theorem of Algebra states that every polynomial equation has at least one root, which may be a real or a complex number.<br />2. If f(x) is of degree n, then there will be n linear factors.<br />3. Every polynomial equation of degree n has exactly n roots.<br />4. Complex roots always occur in conjugate pairs, a+bi and a-bi.<br />5. If the coefficients of the equation <br />
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