11X1 T16 01 definitions
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Transcript of 11X1 T16 01 definitions
![Page 1: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/1.jpg)
Polynomial Functions
![Page 2: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/2.jpg)
Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;
nn
nn xpxpxpxppxP
11
2210
![Page 3: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/3.jpg)
Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;
nn
nn xpxpxpxppxP
11
2210
0 :where np
![Page 4: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/4.jpg)
Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;
nn
nn xpxpxpxppxP
11
2210
0 :where npintegeran isand 0n
![Page 5: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/5.jpg)
Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;
nn
nn xpxpxpxppxP
11
2210
0 :where npintegeran isand 0n
coefficients: 0 1 2, , , , np p p p
![Page 6: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/6.jpg)
Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;
nn
nn xpxpxpxppxP
11
2210
0 :where npintegeran isand 0n
coefficients: 0 1 2, , , , np p p p
index (exponent): the powers of the pronumerals.
![Page 7: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/7.jpg)
Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;
nn
nn xpxpxpxppxP
11
2210
0 :where npintegeran isand 0n
degree (order): the highest index of the polynomial. The polynomial is called “polynomial of degree n”
coefficients: 0 1 2, , , , np p p p
index (exponent): the powers of the pronumerals.
![Page 8: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/8.jpg)
Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;
nn
nn xpxpxpxppxP
11
2210
0 :where npintegeran isand 0n
degree (order): the highest index of the polynomial. The polynomial is called “polynomial of degree n”
coefficients: 0 1 2, , , , np p p p
index (exponent): the powers of the pronumerals.
leading term: nnp x
![Page 9: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/9.jpg)
Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;
nn
nn xpxpxpxppxP
11
2210
0 :where npintegeran isand 0n
degree (order): the highest index of the polynomial. The polynomial is called “polynomial of degree n”
leading coefficient:
coefficients: 0 1 2, , , , np p p p
index (exponent): the powers of the pronumerals.
leading term: nnp x
np
![Page 10: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/10.jpg)
Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;
nn
nn xpxpxpxppxP
11
2210
0 :where npintegeran isand 0n
degree (order): the highest index of the polynomial. The polynomial is called “polynomial of degree n”
leading coefficient: monic polynomial: leading coefficient is equal to one.
coefficients: 0 1 2, , , , np p p p
index (exponent): the powers of the pronumerals.
leading term: nnp x
np
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P(x) = 0: polynomial equation
![Page 12: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/12.jpg)
P(x) = 0: polynomial equationy = P(x): polynomial function
![Page 13: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/13.jpg)
roots: solutions to the polynomial equation P(x) = 0
P(x) = 0: polynomial equationy = P(x): polynomial function
![Page 14: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/14.jpg)
roots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial.
P(x) = 0: polynomial equationy = P(x): polynomial function
![Page 15: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/15.jpg)
roots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial.
P(x) = 0: polynomial equationy = P(x): polynomial function
e.g. (i) Which of the following are polynomials?1
3 2
2
2
a) 5 7 24b)
33c)
4d) 7
x x
xx
![Page 16: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/16.jpg)
roots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial.
P(x) = 0: polynomial equationy = P(x): polynomial function
e.g. (i) Which of the following are polynomials?1
3 2
2
2
a) 5 7 24b)
33c)
4d) 7
x x
xx
NO, can’t have fraction as a power
![Page 17: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/17.jpg)
roots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial.
P(x) = 0: polynomial equationy = P(x): polynomial function
e.g. (i) Which of the following are polynomials?1
3 2
2
2
a) 5 7 24b)
33c)
4d) 7
x x
xx
NO, can’t have fraction as a power
NO, can’t have negative as a power 124 3x
![Page 18: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/18.jpg)
roots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial.
P(x) = 0: polynomial equationy = P(x): polynomial function
e.g. (i) Which of the following are polynomials?1
3 2
2
2
a) 5 7 24b)
33c)
4d) 7
x x
xx
NO, can’t have fraction as a power
NO, can’t have negative as a power 124 3x
YES,21 3
4 4x
![Page 19: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/19.jpg)
roots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial.
P(x) = 0: polynomial equationy = P(x): polynomial function
e.g. (i) Which of the following are polynomials?1
3 2
2
2
a) 5 7 24b)
33c)
4d) 7
x x
xx
NO, can’t have fraction as a power
NO, can’t have negative as a power 124 3x
YES,21 3
4 4x
YES, 07x
![Page 20: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/20.jpg)
roots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial.
P(x) = 0: polynomial equationy = P(x): polynomial function
e.g. (i) Which of the following are polynomials?1
3 2
2
2
a) 5 7 24b)
33c)
4d) 7
x x
xx
NO, can’t have fraction as a power
NO, can’t have negative as a power 124 3x
YES,21 3
4 4x
YES, 07x(ii) Determine whether is
monic and state its degree. 3 2 2( ) 8 1 7 11 2 1 4 3P x x x x x x
![Page 21: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/21.jpg)
roots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial.
P(x) = 0: polynomial equationy = P(x): polynomial function
e.g. (i) Which of the following are polynomials?1
3 2
2
2
a) 5 7 24b)
33c)
4d) 7
x x
xx
NO, can’t have fraction as a power
NO, can’t have negative as a power 124 3x
YES,21 3
4 4x
YES, 07x(ii) Determine whether is
monic and state its degree. 3 2 2( ) 8 1 7 11 2 1 4 3P x x x x x x
4 3 4 2 2( ) 8 7 11 8 6 4 3P x x x x x x x
![Page 22: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/22.jpg)
roots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial.
P(x) = 0: polynomial equationy = P(x): polynomial function
e.g. (i) Which of the following are polynomials?1
3 2
2
2
a) 5 7 24b)
33c)
4d) 7
x x
xx
NO, can’t have fraction as a power
NO, can’t have negative as a power 124 3x
YES,21 3
4 4x
YES, 07x(ii) Determine whether is
monic and state its degree. 3 2 2( ) 8 1 7 11 2 1 4 3P x x x x x x
4 3 4 2 2( ) 8 7 11 8 6 4 3P x x x x x x x 3 22 7 8x x x
![Page 23: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/23.jpg)
roots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial.
P(x) = 0: polynomial equationy = P(x): polynomial function
e.g. (i) Which of the following are polynomials?1
3 2
2
2
a) 5 7 24b)
33c)
4d) 7
x x
xx
NO, can’t have fraction as a power
NO, can’t have negative as a power 124 3x
YES,21 3
4 4x
YES, 07x(ii) Determine whether is
monic and state its degree. 3 2 2( ) 8 1 7 11 2 1 4 3P x x x x x x
4 3 4 2 2( ) 8 7 11 8 6 4 3P x x x x x x x 3 22 7 8x x x monic, degree = 3
![Page 24: 11X1 T16 01 definitions](https://reader033.fdocuments.us/reader033/viewer/2022051513/547c6982b47959ac508b466e/html5/thumbnails/24.jpg)
roots: solutions to the polynomial equation P(x) = 0zeros: the values of x that make polynomial P(x) zero. i.e. the x intercepts of the graph of the polynomial.
P(x) = 0: polynomial equationy = P(x): polynomial function
e.g. (i) Which of the following are polynomials?1
3 2
2
2
a) 5 7 24b)
33c)
4d) 7
x x
xx
NO, can’t have fraction as a power
NO, can’t have negative as a power 124 3x
YES,21 3
4 4x
YES, 07x(ii) Determine whether is
monic and state its degree. 3 2 2( ) 8 1 7 11 2 1 4 3P x x x x x x
4 3 4 2 2( ) 8 7 11 8 6 4 3P x x x x x x x 3 22 7 8x x x monic, degree = 3
Exercise 4A; 1, 2acehi, 3bdf, 6bdf, 7, 9d, 10ad, 13