Hiral polynomials mini

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 !!!