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11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
11 x1 t15 01 definitions (2013)
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11 x1 t15 01 definitions (2013)

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  • 1. Polynomial Functions
  • 2. Polynomial Functions A real polynomial P(x) of degree n is an expression of the form; P x   p0  p1 x  p2 x 2    pn1 x n1  pn x n
  • 3. Polynomial Functions A real polynomial P(x) of degree n is an expression of the form; P x   p0  p1 x  p2 x 2    pn1 x n1  pn x n where : pn  0
  • 4. Polynomial Functions A real polynomial P(x) of degree n is an expression of the form; P x   p0  p1 x  p2 x 2    pn1 x n1  pn x n where : pn  0 n  0 and is an integer
  • 5. Polynomial Functions A real polynomial P(x) of degree n is an expression of the form; P x   p0  p1 x  p2 x 2    pn1 x n1  pn x n where : pn  0 n  0 and is an integer coefficients: p0 , p1 , p2 , , pn
  • 6. Polynomial Functions A real polynomial P(x) of degree n is an expression of the form; P x   p0  p1 x  p2 x 2    pn1 x n1  pn x n where : pn  0 n  0 and is an integer coefficients: p0 , p1 , p2 , , pn index (exponent): the powers of the pronumerals.
  • 7. Polynomial Functions A real polynomial P(x) of degree n is an expression of the form; P x   p0  p1 x  p2 x 2    pn1 x n1  pn x n where : pn  0 n  0 and is an integer coefficients: p0 , p1 , p2 , , pn index (exponent): the powers of the pronumerals. degree (order): the highest index of the polynomial. The polynomial is called “polynomial of degree n”
  • 8. Polynomial Functions A real polynomial P(x) of degree n is an expression of the form; P x   p0  p1 x  p2 x 2    pn1 x n1  pn x n where : pn  0 n  0 and is an integer coefficients: p0 , p1 , p2 , , pn index (exponent): the powers of the pronumerals. degree (order): the highest index of the polynomial. The polynomial is called “polynomial of degree n” n leading term: pn x
  • 9. Polynomial Functions A real polynomial P(x) of degree n is an expression of the form; P x   p0  p1 x  p2 x 2    pn1 x n1  pn x n where : pn  0 n  0 and is an integer coefficients: p0 , p1 , p2 , , pn index (exponent): the powers of the pronumerals. degree (order): the highest index of the polynomial. The polynomial is called “polynomial of degree n” n leading term: pn x leading coefficient: pn
  • 10. Polynomial Functions A real polynomial P(x) of degree n is an expression of the form; P x   p0  p1 x  p2 x 2    pn1 x n1  pn x n where : pn  0 n  0 and is an integer coefficients: p0 , p1 , p2 , , pn index (exponent): the powers of the pronumerals. degree (order): the highest index of the polynomial. The polynomial is called “polynomial of degree n” n leading term: pn x leading coefficient: pn monic polynomial: leading coefficient is equal to one.
  • 11. P(x) = 0: polynomial equation
  • 12. P(x) = 0: polynomial equation y = P(x): polynomial function
  • 13. P(x) = 0: polynomial equation y = P(x): polynomial function roots: solutions to the polynomial equation P(x) = 0
  • 14. P(x) = 0: polynomial equation y = P(x): polynomial function roots: solutions to the polynomial equation P(x) = 0 zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial.
  • 15. P(x) = 0: polynomial equation y = P(x): polynomial function roots: solutions to the polynomial equation P(x) = 0 zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial. e.g. (i) Which of the following are polynomials? 1 2 a) 5 x 3  7 x  2 4 b) 2 x 3 x2  3 c) 4 d) 7
  • 16. P(x) = 0: polynomial equation y = P(x): polynomial function roots: solutions to the polynomial equation P(x) = 0 zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial. e.g. (i) Which of the following are polynomials? 1 2 a) 5 x 3  7 x  2 4 b) 2 x 3 x2  3 c) 4 d) 7 NO, can’t have fraction as a power
  • 17. P(x) = 0: polynomial equation y = P(x): polynomial function roots: solutions to the polynomial equation P(x) = 0 zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial. e.g. (i) Which of the following are polynomials? 1 2 a) 5 x 3  7 x  2 NO, can’t have fraction as a power 4 1 2 b) 2 NO, can’t have negative as a power 4  x  3 x 3 x2  3 c) 4 d) 7
  • 18. P(x) = 0: polynomial equation y = P(x): polynomial function roots: solutions to the polynomial equation P(x) = 0 zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial. e.g. (i) Which of the following are polynomials? 1 2 a) 5 x 3  7 x  2 NO, can’t have fraction as a power 4 1 2 b) 2 NO, can’t have negative as a power 4  x  3 x 3 1 2 3 x2  3 x  c) YES, 4 4 4 d) 7
  • 19. P(x) = 0: polynomial equation y = P(x): polynomial function roots: solutions to the polynomial equation P(x) = 0 zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial. e.g. (i) Which of the following are polynomials? 1 2 a) 5 x 3  7 x  2 NO, can’t have fraction as a power 4 1 2 b) 2 NO, can’t have negative as a power 4  x  3 x 3 1 2 3 x2  3 x  c) YES, 4 4 4 YES, 7x 0 d) 7
  • 20. P(x) = 0: polynomial equation y = P(x): polynomial function roots: solutions to the polynomial equation P(x) = 0 zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial. e.g. (i) Which of the following are polynomials? 1 2 a) 5 x 3  7 x  2 NO, can’t have fraction as a power 4 1 2 b) 2 NO, can’t have negative as a power 4  x  3 x 3 1 2 3 x2  3 x  c) YES, 4 4 4 YES, 7x 0 d) 7 (ii) Determine whether P( x)  x 3  8 x  1  7 x  11   2 x 2  1 4 x 2  3 is monic and state its degree.
  • 21. P(x) = 0: polynomial equation y = P(x): polynomial function roots: solutions to the polynomial equation P(x) = 0 zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial. e.g. (i) Which of the following are polynomials? 1 2 a) 5 x 3  7 x  2 NO, can’t have fraction as a power 4 1 2 b) 2 NO, can’t have negative as a power 4  x  3 x 3 1 2 3 x2  3 x  c) YES, 4 4 4 YES, 7x 0 d) 7 (ii) Determine whether P( x)  x 3  8 x  1  7 x  11   2 x 2  1 4 x 2  3 is monic and state its degree. P( x)  8 x 4  x3  7 x  11  8 x 4  6 x 2  4 x 2  3
  • 22. P(x) = 0: polynomial equation y = P(x): polynomial function roots: solutions to the polynomial equation P(x) = 0 zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial. e.g. (i) Which of the following are polynomials? 1 2 a) 5 x 3  7 x  2 NO, can’t have fraction as a power 4 1 2 b) 2 NO, can’t have negative as a power 4  x  3 x 3 1 2 3 x2  3 x  c) YES, 4 4 4 YES, 7x 0 d) 7 (ii) Determine whether P( x)  x 3  8 x  1  7 x  11   2 x 2  1 4 x 2  3 is monic and state its degree. P( x)  8 x 4  x3  7 x  11  8 x 4  6 x 2  4 x 2  3  x3  2 x 2  7 x  8
  • 23. P(x) = 0: polynomial equation y = P(x): polynomial function roots: solutions to the polynomial equation P(x) = 0 zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial. e.g. (i) Which of the following are polynomials? 1 2 a) 5 x 3  7 x  2 NO, can’t have fraction as a power 4 1 2 b) 2 NO, can’t have negative as a power 4  x  3 x 3 1 2 3 x2  3 x  c) YES, 4 4 4 YES, 7x 0 d) 7 (ii) Determine whether P( x)  x 3  8 x  1  7 x  11   2 x 2  1 4 x 2  3 is monic and state its degree. P( x)  8 x 4  x3  7 x  11  8 x 4  6 x 2  4 x 2  3  monic, degree = 3  x3  2 x 2  7 x  8
  • 24. P(x) = 0: polynomial equation y = P(x): polynomial function roots: solutions to the polynomial equation P(x) = 0 zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial. e.g. (i) Which of the following are polynomials? 1 2 a) 5 x 3  7 x  2 NO, can’t have fraction as a power 4 1 2 b) 2 NO, can’t have negative as a power 4  x  3 x 3 1 2 3 x2  3 Exercise 4A; 1, 2acehi, 3bdf, x  c) YES, 4 4 4 6bdf, 7, 9d, 10ad, 13 0 YES, 7x d) 7 (ii) Determine whether P( x)  x 3  8 x  1  7 x  11   2 x 2  1 4 x 2  3 is monic and state its degree. P( x)  8 x 4  x3  7 x  11  8 x 4  6 x 2  4 x 2  3  monic, degree = 3  x3  2 x 2  7 x  8

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