11 x1 t15 01 polynomial definitions (2012)

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  • 1. Polynomial Functions

2. Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;P x p0 p1 x p2 x 2 pn1 x n1 pn x n 3. Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;P x p0 p1 x p2 x 2 pn1 x n1 pn x nwhere : pn 0 4. Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;P x p0 p1 x p2 x 2 pn1 x n1 pn x nwhere : pn 0n 0 and is an integer 5. Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;P x p0 p1 x p2 x 2 pn1 x n1 pn x n where : pn 0n 0 and is an integercoefficients: p0 , p1 , p2 , , pn 6. Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;P x p0 p1 x p2 x 2 pn1 x n1 pn x n where : pn 0n 0 and is an integercoefficients: p0 , p1 , p2 , , pnindex (exponent): the powers of the pronumerals. 7. Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;P x p0 p1 x p2 x 2 pn1 x n1 pn x n where : pn 0n 0 and is an integercoefficients: p0 , p1 , p2 , , pnindex (exponent): the powers of the pronumerals.degree (order): the highest index of the polynomial. Thepolynomial is called polynomial of degree n 8. Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;P x p0 p1 x p2 x 2 pn1 x n1 pn x n where : pn 0n 0 and is an integercoefficients: p0 , p1 , p2 , , pnindex (exponent): the powers of the pronumerals.degree (order): the highest index of the polynomial. Thepolynomial is called polynomial of degree n nleading term: pn x 9. Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;P x p0 p1 x p2 x 2 pn1 x n1 pn x n where : pn 0n 0 and is an integercoefficients: p0 , p1 , p2 , , pnindex (exponent): the powers of the pronumerals.degree (order): the highest index of the polynomial. Thepolynomial is called polynomial of degree n nleading term: pn xleading coefficient: pn 10. Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;P x p0 p1 x p2 x 2 pn1 x n1 pn x n where : pn 0n 0 and is an integercoefficients: p0 , p1 , p2 , , pnindex (exponent): the powers of the pronumerals.degree (order): the highest index of the polynomial. Thepolynomial is called polynomial of degree n nleading term: pn xleading coefficient: pnmonic polynomial: leading coefficient is equal to one. 11. P(x) = 0: polynomial equation 12. P(x) = 0: polynomial equationy = P(x): polynomial function 13. P(x) = 0: polynomial equationy = P(x): polynomial functionroots: solutions to the polynomial equation P(x) = 0 14. P(x) = 0: polynomial equationy = P(x): polynomial functionroots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the xintercepts of the graph of the polynomial. 15. P(x) = 0: polynomial equation y = P(x): polynomial functionroots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the xintercepts of the graph of the polynomial.e.g. (i) Which of the following are polynomials? 1 a) 5 x 3 7 x 2 24 b) 2 x 3x2 3 c)4 d) 7 16. P(x) = 0: polynomial equation y = P(x): polynomial functionroots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the xintercepts of the graph of the polynomial.e.g. (i) Which of the following are polynomials? 1 a) 5 x 3 7 x 2 2 NO, cant have fraction as a power4 b) 2 x 3x2 3 c)4 d) 7 17. P(x) = 0: polynomial equation y = P(x): polynomial functionroots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the xintercepts of the graph of the polynomial.e.g. (i) Which of the following are polynomials? 1 a) 5 x 3 7 x 2 2 NO, cant have fraction as a power4NO, cant have negative as a power 4 x 31 b) 2 2 x 3x2 3 c)4 d) 7 18. P(x) = 0: polynomial equation y = P(x): polynomial functionroots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the xintercepts of the graph of the polynomial.e.g. (i) Which of the following are polynomials? 1 a) 5 x 3 7 x 2 2NO, cant have fraction as a power4NO, cant have negative as a power 4 x 31 b) 2 2 x 3x2 31 2 3 c)YES, x 4 4 4 d) 7 19. P(x) = 0: polynomial equation y = P(x): polynomial functionroots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the xintercepts of the graph of the polynomial.e.g. (i) Which of the following are polynomials? 1 a) 5 x 3 7 x 2 2NO, cant have fraction as a power4NO, cant have negative as a power 4 x 31 b) 2 2 x 3x2 31 2 3 c)YES, x 4 4 4 d) 7YES, 7x 0 20. P(x) = 0: polynomial equation y = P(x): polynomial functionroots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the xintercepts of the graph of the polynomial.e.g. (i) Which of the following are polynomials?1a) 5 x 3 7 x 22 NO, cant have fraction as a power 4 NO, cant have negative as a power 4 x 31b) 22x 3 x2 31 2 3c)YES, x 4 4 4d) 7YES, 7x 0(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 functionroots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the xintercepts of the graph of the polynomial.e.g. (i) Which of the following are polynomials?1 a) 5 x 3 7 x 22 NO, cant have fraction as a power 4NO, cant have negative as a power 4 x 31 b) 2 2 x 3 x2 31 2 3 c)YES,x 444 d) 7YES, 7x 0(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 functionroots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the xintercepts of the graph of the polynomial.e.g. (i) Which of the following are polynomials?1 a) 5 x 3 7 x 22 NO, cant have fraction as a power 4NO, cant have negative as a power 4 x 31 b) 2 2 x 3 x2 31 2 3 c)YES,x 444 d) 7YES, 7x 0(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 functionroots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the xintercepts of the graph of the polynomial.e.g. (i) Which of the following are polynomials?1 a) 5 x 3 7 x 22 NO, cant have fraction as a power 4NO, cant have negative as a power 4 x 31 b) 2 2 x 3 x2 31 2 3 c)YES,x 444 d) 7YES, 7x 0(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 monic, degree = 3 24. P(x) = 0: polynomial equation y = P(x): polynomial functionroots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the xintercepts of the graph of the polynomial.e.g. (i) Which of the following are polynomials?1 a) 5 x 3 7 x 22 NO, cant have fraction as a power 4NO, cant have negative as a power 4 x 31 b) 2 2 x 3 x2 31 2 3 c)YES,x Exercise 4A; 1, 2acehi, 3bdf,4446bdf, 7, 9d, 10ad, 13 0 d) 7YES, 7x(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 monic, degree = 3