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MATHAMATICS

Title:PolynomialPresented By:Lekhamol V RRoll No:22,1st Year B.Ed Option: Mathematics

1. Be able to determine the degree of a polynomial.

2. Be able to classify a polynomial.3. Be able to write a polynomial in standard

form.

Monomial: A number, a variable or the product of a number and one or more variables.

Polynomial: A monomial or a sum of monomials.

Binomial: A polynomial with exactly two terms.

Trinomial: A polynomial with exactly three terms.

Coefficient: A numerical factor in a term of an algebraic expression.

Degree of a monomial: The sum of the exponents of all of the variables in the monomial.

Degree of a polynomial in one variable: The largest exponent of that variable.

Standard form: When the terms of a polynomial are arranged from the largest exponent to the smallest exponent in decreasing order.

What is the degree of the monomial? 245 bx

The degree of a monomial is the sum of the exponents of the variables in the monomial.

The exponents of each variable are 4 and 2. 4+2 = 6.

The degree of the monomial is 6. The monomial can be referred to as a sixth

degree monomial.

A polynomial is a monomial or the sum of monomials

24x 83 3 x 1425 2 xx Each monomial in a polynomial is a term of the

polynomial. The number factor of a term is called the

coefficient. The coefficient of the first term in a

polynomial is the lead coefficient. A polynomial with two terms is called a

binomial. A polynomial with three terms is called a

trinomial.

14 x

83 3 x

1425 2 xx

The degree of a polynomial in one variable is the largest exponent of that variable.

2 A constant has no variable. It is a 0 degree polynomial.

This is a 1st degree polynomial. 1st degree polynomials are linear.

This is a 2nd degree polynomial. 2nd degree polynomials are quadratic.

This is a 3rd degree polynomial. 3rd degree polynomials are cubic.

Classify the polynomials by degree and number of terms.

Polynomiala.

b.

c.

d.

5

42 x

xx 23

14 23 xx

DegreeClassify by

degree

Classify by number of

termsZero Constant Monomial

First Linear Binomial

Second Quadratic Binomial

Third Cubic Trinomial

To rewrite a polynomial in standard form, rearrange the terms of the polynomial starting with the largest degree term and ending with the lowest degree term.

The leading coefficient, the coefficient of the first term in a polynomial written in standard form, should be positive.

745 24 xxx

x544x 2x 7

Write the polynomials in standard form.

243 5572 xxxx

32x4x 7x525x

)7552(1 234 xxxx

32x4x 7x525x

Remember: The lead coefficient should be positive in standard

form.To do this, multiply

the polynomial by –1 using the distributive

property.

Write the polynomials in standard form and identify the polynomial by degree and number of terms.

23 237 xx 1.

2. xx 231 2

23 237 xx

23 237 xx

33x 22x 7

7231 23 xx

723 23 xx

This is a 3rd degree, or cubic, trinomial.

xx 231 2

xx 231 2

23x x2 1

This is a 2nd degree, or quadratic, trinomial.

Add: (x2 + 3x + 1) + (4x2 +5)

Step 1: Underline like terms:

Step 2: Add the coefficients of like terms, do not change the powers of the variables:

Adding Polynomials

(x2 + 3x + 1) + (4x2 +5)

Notice: ‘3x’ doesn’t have a like term.

(x2 + 4x2) + 3x + (1 + 5)5x2 + 3x + 6

Some people prefer to add polynomials by stacking them. If you choose to do this, be sure to line up the like terms!

Adding Polynomials

(x2 + 3x + 1) + (4x2 +5) 5x2 + 3x + 6

(x2 + 3x + 1) + (4x2 +5)

Stack and add these polynomials: (2a2+3ab+4b2) + (7a2+ab+-2b2)(2a2+3ab+4b2) + (7a2+ab+-2b2)

(2a2 + 3ab + 4b2) + (7a2 + ab + -

2b2)9a2 + 4ab + 2b2

Adding Polynomials

1) 3x3 7x 3x3 4x 6x3 3x

2) 2w2 w 5 4w2 7w 1 6w2 8w 4

3) 2a3 3a2 5a a3 4a 3 3a3 3a2 9a 3

• Add the following polynomials; you may stack them if you prefer:

Subtract: (3x2 + 2x + 7) - (x2 + x + 4)

Subtracting Polynomials

Step 1: Change subtraction to addition (Keep-Change-Change.).

Step 2: Underline OR line up the like terms and add.

(3x2 + 2x + 7) + (- x2 + - x + - 4)

(3x2 + 2x + 7) + (- x2 + - x + - 4)

2x2 + x + 3

Subtracting Polynomials

1) x2 x 4 3x 2 4x 1 2x2 3x 5

2) 9y2 3y 1 2y2 y 9 7y2 4y 10

3) 2g2 g 9 g3 3g2 3 g3 g2 g 12

• Subtract the following polynomials by changing to addition (Keep-Change-Change.), then add:

THANK YOU