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# 11 x1 t15 01 definitions (2013)

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### 11 x1 t15 01 definitions (2013)

1. 1. Polynomial Functions
2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 11. P(x) = 0: polynomial equation
12. 12. P(x) = 0: polynomial equation y = P(x): polynomial function
13. 13. P(x) = 0: polynomial equation y = P(x): polynomial function roots: solutions to the polynomial equation P(x) = 0
14. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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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