hiral polynomials mini
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K.J. Somaiya Comprehensive College of Education, Training and
Research.
Name – Hiral Thaker.Std – VIIIth.
Roll No. – 72.Year 2010 – 2011
What does each prefix mean?mono
one
bi
two
tri
three
poly
one or more
Polynomial
ObjectivesThe student will be able to:
1. Define polynomial.
2. Classify polynomial.
3. Find the degree of a polynomial.
Polynomialone or more
A polynomial is a mathematical expression with one or more terms and index of every variable has to be a whole number.
Eg. 1. 5x3
2. 8y + 7z2
3. m2 – 3m + 4
Important Note!!
An expression is not a polynomial if there is a variable in the denominator or the index
of the variable is negative or a fraction.
• Eg. 4x – 7x-2
10m + 7m7/2
Classification of polynomials
Polynomial
Monomial Binomial Trinomial
Monomial
A polynomial of only one term is called a monomial.
Eg. -17.
62p.
53a4b3c.
Binomial
A polynomial of two terms is called a binomial.
Eg. 3p + 9.
4 – 5a.
17 – b3.
Trinomial
A polynomial of three terms is called trinomial.
Eg. x2 + 2x + 2.
a - 9 + 2a2 .
13 + n3 – 6n.
State whether each expression is a polynomial. If it is, identify it.
1) 7y - 3x + 4
trinomial
2) 10x3yz2
monomial
3)
not a polynomial2
57
2y
y
Which polynomial is represented by
X2
1
1
X
X
X
1. x2 + x + 1
2. x2 + x + 2
3. x2 + 2x + 2
4. x2 + 3x + 2
5. I’ve got no idea!
The degree of a monomial is the sum of the exponents of the variables.
Find the degree of each monomial.1) 5x2
2
2) 4a4b3c
8
3) -3
0
To find the degree of a polynomial, find the largest degree of the terms.
1) 8x2 - 2x + 7
Degrees: 2 1 0
Which is biggest? 2 is the degree!
2) y7 + 6y4 + 3x4m4
Degrees: 7 4 8
8 is the degree!
Find the degree of x5 – x3y2 + 4
1. 0
2. 2
3. 3
4. 5
5. 10
Evaluation ???
Q.1)Define polynomial.
Ans. A polynomial is a mathematical expression with one or more terms and index of every variable has to be a whole number.
Q.2)Are the following expression polynomials ?
• 4a4 + a3 - 14.
Ans. Yes, it is a polynomial.
• 12 + 10 p-2
Ans. No, it is not a polynomial.
Q.3) State the degree of polynomial
1) x3 - 2x + 7
Degrees: 3 1 0
Which is biggest? 3 is the degree!
2) 8y7 + y4 + x3m4
Degrees: 7 4 7
7 is the degree!
Thank You !!!