11 x1 t15 01 definitions (2013)
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Transcript of 11 x1 t15 01 definitions (2013)
Polynomial Functions
Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;
nn
nn xpxpxpxppxP
11
2210
Polynomial FunctionsA real polynomial P(x) of degree n is an expression of the form;
nn
nn xpxpxpxppxP
11
2210
0 :where np
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
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
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.
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.
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
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
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
P(x) = 0: polynomial equation
P(x) = 0: polynomial equationy = P(x): polynomial function
roots: solutions to the polynomial equation P(x) = 0
P(x) = 0: polynomial equationy = P(x): polynomial function
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
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
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
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
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
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
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
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
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
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
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