Introduction to Polynomials 5.2 1.Identify monomials. 2.Identify the coefficient and degree of a...
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Transcript of Introduction to Polynomials 5.2 1.Identify monomials. 2.Identify the coefficient and degree of a...
Introduction to Polynomials5.25.2
1. Identify monomials.2. Identify the coefficient and degree of a monomial.3. Classify polynomials.4. Identify the degree of a polynomial.5. Evaluate polynomials.6. Write polynomials in descending order of degree.7. Combine like terms.
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.
Exponent can’t be negative!Exponent can’t have fractions!
a numberx, y
Multiply a number and a
variable
When an equation in one variable is solved the answer is a point on a line.
Is the given expression a monomial?Is the given expression a monomial?
18
34 x
b0.4a– 2
x3
YesYes
No No
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.
When an equation in one variable is solved the answer is a point on a line.
Identify the coefficient and degree of each monomial:Identify the coefficient and degree of each monomial:
28p
18
m-
276 uv.
532 a 24
C: -1D: 1
C: 8D: 2
C: 18D: 0
C: -6.7D: 3
C: 23 = 8D: 5
C: 16D: 0
x0
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.
When an equation in one variable is solved the answer is a point on a line.
Identify the type of polynomial and the degree:Identify the type of polynomial and the degree:
24ab
134 3 nn
z9x- 2
49 23 xxx
xy
68 jjjj 142116522 423
MonomialD: 3
BinomialD: 2
TrinomialD: 3
PolynomialD: 3
Not a polynomial PolynomialD: 4
Evaluate each of the following:Evaluate each of the following:
y,x for yx 412 2
212 b,a for ba
43 n for nn2
-2(-1)2(4) = -8
(-4)2 – (-4) – 3 = 16 + 4 – 3 = 17
- (-1)2 (2) = - (1)(2) = -2
Writing a Polynomial in Descending Order of DegreePlace the highest degree term first, then the next highest degree, and so on.
Combine like terms and write the resulting polynomial in descending order of degree.
3 2 3 34 6 3 7 4 3 6x x x x x x
5 2 5 26 2 3 1 3 3 a a b b a b a b
38x
532 25 baa
26x x2 4
Slide 5- 18Copyright © 2011 Pearson Education, Inc.
Classify the expression
a) Monomial
b) Binomial
c) Trinomial
d) None of these
2 33 5.x y
5.2
Slide 5- 19Copyright © 2011 Pearson Education, Inc.
Classify the expression
a) Monomial
b) Binomial
c) Trinomial
d) None of these
2 33 5.x y
5.2
Slide 5- 20Copyright © 2011 Pearson Education, Inc.
Evaluate when x = –3.
a) –118
b) –10
c) 10
d) 134
3 23 5 8 x x
5.2
Slide 5- 21Copyright © 2011 Pearson Education, Inc.
Evaluate when x = –3.
a) –118
b) –10
c) 10
d) 134
3 23 5 8 x x
5.2
Slide 5- 22Copyright © 2011 Pearson Education, Inc.
Identify the degree of the polynomial.
a) 3
b) 5
c) 6
d) 7
3 2 4 6 56 5 8 4 x x y x y y
5.2