powercab 1polynomial function
TRANSCRIPT
POLYNOMIAL
FUNCTION
A polynomial function of a degree n is a
function of the form
F(x)= An , An-1 Xn-1,A n-2X n-2 + . . . + A0
When n is a nonnegative integer and
An , An-1 Xn-1,A n-2X n-2 + . . . + A0 are real
numbers , and ≠ 0.
PARTS
Number of termsdetermined by the highest power
of its term
Example:
F(x)=2x 5 + x 2 –x + 2
Therefore, the degree (n) of f(x) is
5
Leading CoefficientExample:
F(x) =8x 5 + 3x 4 + x – 10
Therefore, the leading coefficient (An)
of f(x) is 8
Leading Term
Example:
F(x) =8x 5 + 3x 4 + x – 10
Therefore, the leading
coefficient (An) of f(x) is 8
Constant TermExample:
F(x)= x 5 – x 4 + 4x +3
Therefore, constant term
(A0) of f(x) is 3
By the Number ofTerms
Monomials consists of only one term
Example:
2x 3 ,5 , 6x 4 y, -4xy,…
Binomial consists of two terms
Example:
2a+b,x 2 + y 2 ,2x 3 + 6xy,
. ..
Trinomials
consists of three termsExample:
X 2-2x +7, 5a 2 b 2 – 20, . . .
Multinomialconsists of four or more terms
Example:
8x 5 + 5x 2 + y +2y, 7x 3
y – y 3 +2x 4 y -3x,. . .
KINDS
By the Highest Power /
Degree
Linearpolynomial with a highest
power of oneExample:
7x+y, 3x ,5x+6
Quadraticpolynomial with a highest
power of twoExample:
X 2 + 7x + 10, X 2 + 9, X 2
+ y, . .
Cubicpolynomial with a highest
power of threeExample:
x 3 + 8, x 3 + 4x 2 +5x + 8,
. . .
Quarticpolynomial with a highest
power of fourExample:
7x 4 +2x 3 + 6x 2 +10, 8x 4
+9, . . .
Penticpolynomial with a highest
power of fiveExample:
10x 5 + 5,6x 5 +2x 3
+7,. . .
