# Introduction to polynomial class 10th #

#polynomial#
*Class 10th*

1. Introduction to Polynomials5.2
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.

2. Objective1
Identify monomials.

3. 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

4. When an equation in one variable is solved the answer is a point on a line.
Is the given expression a monomial?18 3
4

x b0.4a–
2 x
3
Yes
Yes
No No

5. Objective2
Identify the coefficient and degree of
a monomial.

6. Coefficient of a monomial:The numerical
factor in a monomial.
Degree of a monomial:The sum of the
exponents of all variablesin a monomial.

7. When an equation in one variable is solved the answer is a point on a line.
Identify the coefficient and degree of each monomial:2
8p 18 m- 2
76uv. 53
2a 2
4
C: -1
D: 1
C: 8
D: 2
C: 18
D: 0
C: -6.7
D: 3
C: 2
3
= 8
D: 5
C: 16
D: 0
x
0

8. Objective3
Classify polynomials.
Objective4
Identify the degree of a polynomial.

9. Polynomial:A monomial or an expression that
can be written as a sum of monomials.
Examples: 4x, 4x+ 8, 2x
2
-5xy+ 8y
Polynomial in one variable:A polynomial in
which every variable term has the same
variable.
Example: x
2
–5x+ 2

10. 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.

11. When an equation in one variable is solved the answer is a point on a line.
Identify the type of polynomial and the degree:2
4ab 134
3
nn z9x-
2
 49
23
 xxx x
y
6
8 jjjj 142116522
423

Monomial
D: 3
Binomial
D: 2
Trinomial
D: 3
Polynomial
D: 3
Not a polynomial
Polynomial
D: 4

12. Objective5
Evaluate polynomials.

13. Evaluate each of the following: y,x for yx 412
2
 21
2
 b,a for ba 43  n for nn
2
-2(-1)
2
(4) = -8
(-4)
2
–(-4) –3 = 16 + 4 –3 = 17
-(-1)
2
(2) = -(1)(2) = -2

14. Objective6
Write polynomials in descending
order of degree.
Combine like terms.
Objective7

15. Writing a Polynomial in Descending Order of Degree
Place the highest degree term first, then the next
highest degree, and so on.

16. Write the polynomial in descending order.2 3 4
2 5 7 4    x x x x 4
4x 3
x 2
7x x2 5

17. Combine like terms and write the resulting polynomial
in descending order of degree.3 2 3 3
4 6 3 7 4 3 6x x x x x x       5 2 5 2
6 2 3 1 3 3      a a b b a b a b 3
8x 532
25
baa 2
6x x2 4

18. Slide 5-18Copyright © 2011 Pearson Education, Inc.
Classify the expression
a) Monomial
b) Binomial
c) Trinomial
d) None of these 23
3 5.xy
5.2

19. Slide 5-19Copyright © 2011 Pearson Education, Inc.
Classify the expression
a) Monomial
b) Binomial
c) Trinomial
d) None of these 23
3 5.xy
5.2

20. Slide 5-20Copyright © 2011 Pearson Education, Inc.
Evaluate when x= –3.
a) –118
b) –10
c) 10
d) 134 32
3 5 8xx
5.2

21. Slide 5-21Copyright © 2011 Pearson Education, Inc.
Evaluate when x= –3.
a) –118
b) –10
c) 10
d) 134 32
3 5 8xx
5.2

22. 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 5
6 5 8 4  x x y x y y
5.2

23. Slide 5-23Copyright © 2011 Pearson Education, Inc.
Identify the degree of the polynomial.
a) 3
b) 5
c) 6
d) 7 3 2 4 6 5
6 5 8 4  x x y x y y
5.2