Download 2.1 - Polynomial Characteristics

LET’S BEGIN!!!

LET’S REVIEW FUNCTIONS
Daily Questions…….
1. How do I name polynomials?
2. How do I add and subtract polynomials?
3. How do I multiply polynomials?
POLYNOMIAL Function:
•
A polynomial is the monomial or the sum
of monomials with all exponents as
whole numbers and coefficients are all
real numbers.
• Ex-
x3+6x2+12x+8
Is it a polynomial?
a)
f  x   x  3x
b)
f  x   x  3x  2x  5
c)
f  x   6x  2 x  x
d)
f  x   0.5 x   x  2
YES
3
4
2
4
1
2
x
NO
NO
YES
STANDARD FORM
The terms of a polynomial are in
STANDARD FORM when:
•
they are ordered from left to right in
decreasing
______________
order; which means from
largest
the ____________
exponent to the
smallest
____________
DEGREE:
largest
The _________exponent
in the polynomial. It
Number of Zeros
determines the _____________________.
2
Ex: The degree of –7x + 9 – 4x2 is ____.
Classifying:
x0 x1 x2
0 – Constant
2 – Quadratic
1 – Linear
3 – Cubic
x3
x4
4 - Quartic
LEADING COEFFICIENT:
first coefficient
standard form
The ______________once
in _________________.
CONSTANT:
without
The term _________________
a variable.
STANDARD FORM
a.
2x 2  4  3x 4  12x 3
Standard Form:
Leading Coefficient:
3x 4  12x 3  2x 2  4
Degree (number and name):
3
Constant:
4,quartic
b.
3x
Standard Form:
x  3
Degree:
1,linear
4
Leading Coefficient:
1
Constant:
3
Some polynomials have SPECIAL NAMES that
are determined by the following:
degree
A. Their _________
or
B. Their _________
of terms
number
C. Look at the chart for an explanation.
Polynomial
# of
Name by # DEGREE Name by
Terms of Terms
Degree
12
1
Monomial
0
Constant
8x
1
Monomial
1
Linear
4x2 + 3
2
Binomial
2
Quadratic
5x3 + x2
2
Binomial
3
Cubic
3x2 – 4x + 6
3
Trinomial
2
Quadratic
7t4 – 7t + 3
3
Trinomial
4
Quartic
ADDING AND
SUBTRACTING
POLYNOMIALS
ADDING:
• Combine like terms!
SUBTRACTING:
• Distribute the negative
• Combine like terms!
EX. 1
 4y
3
 5y
2
  12y
5
3
 2y  14y
12y 5  2y 3  9y 2
2

EX. 2
 3y
5
3
 8y  10y
2
   12y
5
3
 4y  14y
15y 5  4y 3  24y 2
2

MULTIPLYING POLYNOMIALS
MULTIPLYING:
• Distribute every term.
Remember: 2 Binomials Make a
Trinomial!
EX. 1
 3m  1 8m  7 
2
24m  13m  7
EX. 2
 x
2

 2x  4  x  3
3
2
 x  5 x  2 x  12
EX. 3
 x  1 x  4  x  3 
3
2
x  6 x  5 x  12
HOMEWORK
Textbook –
Page 333 #15-26 all
Page 341 #13-51 odd