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.
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
2
a) 5 x 3 7 x 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
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.
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.
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.
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.
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.
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.
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.
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.
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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