# 11x1 t13 01 polynomial definitions

Post on 01-Dec-2014

1.161 views

Category:

## Education

Embed Size (px)

DESCRIPTION

TRANSCRIPT

• 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 pn1 x n1 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 pn1 x n1 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 pn1 x n1 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 pn1 x n1 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 pn1 x n1 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 pn1 x n1 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 pn1 x n1 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 pn1 x n1 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 pn1 x n1 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 a) 5 x 3 7 x 2 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 a) 5 x 3 7 x 2 2 NO, cant have fraction as a power 4 b) 2 x 3 x2 3 c) 4 d) 7
• 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 a) 5 x 3 7 x 2 2 NO, cant have fraction as a power 4 NO, cant have negative as a power 4 x 3 1 b) 2 2 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 a) 5 x 3 7 x 2 2 NO, cant have fraction as a power 4 NO, cant have negative as a power 4 x 3 1 b) 2 2 x 3 x2 3 1 2 3 c) YES, x 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 a) 5 x 3 7 x 2 2 NO, cant have fraction as a power 4 NO, cant have negative as a power 4 x 3 1 b) 2 2 x 3 x2 3 1 2 3 c) YES, x 4 4 4 d) 7 YES, 7x 0
• 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 a) 5 x 3 7 x 2 2 NO, cant have fraction as a power 4 NO, cant have negative as a power 4 x 3

Recommended