Polynomials Add And Subtract Ch 9.1

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.

4. Be able to add and subtract polynomials

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.

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.

Polynomial

a.

b.

c.

d.

5

42 x

xx 23

14 23 xx

DegreeNumber of

Terms

Classify by number of

terms

Zero 1 Monomial

First 2 Binomial

Second 2 Binomial

Third 3 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

33x 22x 7

7231 23 xx

723 23 xx

This is a trinomial. The trinomial’s degree is 3.

xx 231 2

23x x2 1

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

Find the Sum

Add (x2 + x + 1) to (2x2 + 3x + 2)

You might decide to add like terms as the next slide demonstrates.

Add Like Terms

+ 2x2 + 3x + 2x2 + x + 1 = 3x2+ 4x+3

Or you could add the trinomials in a column

Just like adding like-terms

+ 2x2 + 3x + 2

x2 + x + 1

3x2 + 4x +3

Start with the trinomials in a column

+ 2x2 + 3x + 2

Combine the trinomials going down

Problem #2

Try one.(3x2+5x) + (4 -6x -2x2)

Make sure you put the polynomials in standard form and line them up by degree.

(3x2+5x) + (4 -6x -2x2)

3x2+5x-2x2 -6x + 4

+ 0 It might be helpful to use a zero as a placeholder.

x2 -x + 4

Find the difference

- (3x2 - 2x + 3)

x2 + 2x - 4

-2x2 + 4x - 7

Start with the trinomials in a column

- (3x2 - 2x + 3)

The negative sign outsideof the parentheses is reallya negative 1 that is multipliedby all the terms inside.

- 3x2 + 2x - 3)

Try One.

- (10x2 + 3x + 2)

12x2 +5x + 11

2x2 + 2x + 9

Reminder:Start with the trinomials in a column

- (10x2 + 3x + 2)

The negative sign outsideof the parentheses is reallya negative 1 that is multipliedby all the terms inside.

- 10x2 - 3x - 2

Special Thanks

to Public Television Station KLVX for the basic outline of the first 12 slides of this presentation