Transcript 5.2 1. 2. 3. 4. 5. 6. 7. Introduction to Polynomials Identify monomials. Identify the coefficient and degree of a monomial. Classify polynomials. Identify the degree of a polynomial. Evaluate polynomials. Write polynomials in.

5.2
1.
2.
3.
4.
5.
6.
7.
Introduction to Polynomials
Identify monomials.
Identify the coefficient and degree of a monomial.
Classify polynomials.
Identify the degree of a polynomial.
Evaluate polynomials.
Write polynomials in descending order of degree.
Combine like terms.
Objective 1
Identify monomials.
a number
x, y
Monomial: An expression that is a constant, a
variable, or a product of a constant and
variable(s) that are raised to whole number
powers.
Multiply a
number and a
variable
Exponent can’t be negative!
Exponent can’t have fractions!
Is the given expression a monomial?
18
2
– 0.4a b
Yes
Yes
When an equation in one variable is solved the answer is a point on a line.
 4x
3
x
3
No
No
Objective 2
Identify the coefficient and degree of
a monomial.
Coefficient of a monomial: The numerical
factor in a monomial.
Degree of a monomial: The sum of the
exponents of all variables in a monomial.
Identify the coefficient and degree of each monomial:
2
8p
-m
C: 8
D: 2
C: -1
D: 1
C:one18
When an equation
in
variable is solved the answer is a point
C:.
x0
2 on a line
18
 6.7uv
D: 0
3 5
2 a
23 =
C:
D: 5
8
4
-6.7
D: 3
2
C: 16
D: 0
Objective 3
Classify polynomials.
Objective 4
Identify the degree of a polynomial.
Polynomial: A monomial or an expression that
can be written as a sum of monomials.
Examples: 4x, 4x + 8,
2x2 - 5xy + 8y
Polynomial in one variable: A polynomial in
which every variable term has the same
variable.
Example: x2 – 5x + 2
Binomial: A polynomial containing two terms.
Trinomial: A polynomial containing three terms.
Degree of a polynomial: The greatest degree of
any of the terms in the polynomial.
Identify the type of polynomial and the degree:
2
4ab
Monomial
D: 3
4n3  3n  1
- 9x2  z
Binomial
D: 2
x 3  9 x2  x  4
When an equation in one variable is solved the answer is a point on a line.
Trinomial
D: 3
6
8y 
x
Not a polynomial
Polynomial
D: 3
22 j3  5j2  16 j4  21  14 j
Polynomial
D: 4
Objective 5
Evaluate polynomials.
Evaluate each of the following:
2
 2x y for x  1, y  4
-2(-1)2(4) = -8
n2  n  3
for n  4
(-4)2 – (-4) – 3 = 16 + 4 – 3 = 17
 a2b
for a  1, b  2
- (-1)2 (2) = - (1)(2) = -2
Objective 6
Write polynomials in descending
order of degree.
Objective 7
Combine like terms.
Writing a Polynomial in Descending Order of Degree
Place the highest degree term first, then the next
highest degree, and so on.
Write the polynomial in descending order.
2 x  5  7 x2  x3  4 x4
4x 4  x 3  7x 2 2x 5
Combine like terms and write the resulting polynomial
in descending order of degree.
4 x 3  6 x 2  3x 3  7  4 x  x 3  3  6 x
8x 3  6x 2 2x 4
6  a5  2a 2b  3b  1  3a5  3b  a 2b
2a 5  3a2 b  5
Classify the expression 3x2 y3  5.
a) Monomial
b) Binomial
c) Trinomial
d) None of these
5.2
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Slide 5- 18
Classify the expression 3x2 y3  5.
a) Monomial
b) Binomial
c) Trinomial
d) None of these
5.2
Copyright © 2011 Pearson Education, Inc.
Slide 5- 19
Evaluate 3x  5 x  8 when x = –3.
3
2
a) –118
b) –10
c) 10
d) 134
5.2
Copyright © 2011 Pearson Education, Inc.
Slide 5- 20
Evaluate 3x  5 x  8 when x = –3.
3
2
a) –118
b) –10
c) 10
d) 134
5.2
Copyright © 2011 Pearson Education, Inc.
Slide 5- 21
Identify the degree of the polynomial.
6 x  5x y  8x y  4 y
3
2
4
6
5
a) 3
b) 5
c) 6
d) 7
5.2
Copyright © 2011 Pearson Education, Inc.
Slide 5- 22
Identify the degree of the polynomial.
6 x  5x y  8x y  4 y
3
2
4
6
5
a) 3
b) 5
c) 6
d) 7
5.2
Copyright © 2011 Pearson Education, Inc.
Slide 5- 23