Ch 8-5 Adding and Subtracting Polynomials

8/13/2019 Ch 8-5 Adding and Subtracting Polynomials

1/13

Algebra tiles can be used to model polynomials.

These 1-by-1square

tiles have an area of

1square unit.

These 1-by-xrectangular

tiles have an area of x

square units.

These x-by-xrectangular

tiles have an area of x2

square units.

+ + +

1 1 x x x2 x2

MODELING ADDITION OF POLYNOMIALS


2/13

You can use algebra tiles to add the polynomials x2+ 4x+ 2and 2x23x1.

+ +

MODELING ADDITION OF POLYNOMIALS

+ + + +

+

+ +

1 Form the polynomials x2+ 4x+ 2and 2x23x1with algebra tiles.

x2 + 4x + 2

2x2 3x 1


3/13

MODELING ADDITION OF POLYNOMIALSYou can use algebra tiles to add the polynomials x2+ 4x+ 2and 2x23x1.

+ + + + + +

+

+ +

x2+ 4x+ 2 2x23x1

2 To add the polynomials, combine like terms. Group the x2-tiles, the x-tiles,

and the 1-tiles.

+

+ +

+

+

+ + + +

+

+

=


4/13

MODELING ADDITION OF POLYNOMIALSYou can use algebra tiles to add the polynomials x2+ 4x+ 2and 2x23x1.

+ + + + + +

+

+ +

x2+ 4x+ 2 2x23x1

2 To add the polynomials, combine like terms. Group the x2-tiles, the x-tiles,

and the 1-tiles.

+

+ +

+

+

+ + + +

+

+

=

3 Find and remove the zero pairs.

The sum is 3x2+ x+ 1.


5/13

An expression which is the sum of terms of the form axkwhere kis a nonnegative

integer is a polynomial. Polynomials are usually written in standard form.

Add ing and Subtract ing Polynom ials

Standard form means that the terms of the polynomial are placed in descending

order, from largest degree to smallest degree.

The degreeof each term of a polynomial is the exponent of the variable.

Polynomial in standard form:

2x3+ 5x24x+ 7

Degree Constant termLeading coefficient

The degree of a polynomialis the largest degree of its terms. When a

polynomial is written in standard form, the coefficient of the first term is

the leading coefficient.


6/13

A polynomial with only one term is called a monomial. A polynomial with two terms

is called a binomial. A polynomial with three terms is called a trinomial. Identify

the following polynomials:

Class i fy ing Polynom ials

Polynomial Degree

Classified by

degree

Classified by

number of terms

6

2x

3x+ 1

x2+ 2x5

4x38x

2x47x35x+ 1

0

1

1

4

2

3

constant

linear

linear

quartic

quadratic

cubic

monomial

monomial

binomial

polynomial

trinomial

binomial


7/13

Find the sum. Write the answer in standard format.(5x3

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

4x) + (4x2

8

x3)

Adding Polynom ials

SOLUTION

Vertical format: Write each expression in standard form. Align like terms.

5x3+ 2x2 x+ 7

3x24x+ 7

x3 + 4x2 8+

4x3+ 9x25x+ 6


8/13

Find the sum. Write the answer in standard format.(2x2+ x

5) + (x+ x2+ 6)

Adding Polynom ials

SOLUTION

Horizontal format: Add like terms.

(2x2+ x5) + (x+ x2+ 6) = (2x2+x2) + (x+ x) + (5+ 6)

= 3x2+ 2x+ 1


9/13

Find the difference.(

2x3+ 5x2

x+ 8)

(

2x2+ 3x4)

Subtract ing Polynom ials

SOLUTION

Use a vertical format. To subtract, you add the opposite. This means you

multiply each term in the subtracted polynomial by

1and add.

2x3+ 5x2 x+ 8

2x3 + 3x4 Add the oppos i te

No change2x3+ 5x2 x+ 8

2x3 3x+ 4+


10/13

Find the difference.(

2x3+ 5x2

x+ 8)

(

2x2+ 3x4)


SOLUTION

Use a vertical format. To subtract, you add the opposite. This means you

multiply each term in the subtracted polynomial by

1and add.

2x3+ 5x2 x+ 8

2x3 + 3x4

5x2

4x+ 12

2x3+ 5x2 x+ 8

2x3 3x+ 4+


11/13

Find the difference.(3x2

5x+ 3)

(2x2

x

4)


SOLUTION

Use a horizontal format.

(3x25x+ 3)(2x2x4) = (3x25x+ 3) + (1)(2x2x4)

=x2

4x+ 7

= (3x25x+ 3)2x2+ x+ 4

= (3x22x2)+ (5x+x) + (3+4)


12/13

Total Area= (10x)(14x2) (square inches)

Area of photo=

You are enlarging a 5-inch by 7-inch photo by a scale factor of xand mounting it on

a mat. You want the mat to be twice as wide as the enlarged photo and 2inches

less than twice as high as the enlarged photo.

Using Polyn om ials in Real Life

Write a model for the area of the mat around the photograph as a function of the

scale factor.

Verbal Model

Labels

Area of mat =Area of

photo

Area of mat = A

(5x)(7x)

(square inches)

(square inches)

Total Area

Use a verbal model.

5x

7x

14x

2

10x

SOLUTION


13/13

(10x)(14x2)(5x)(7x)

You are enlarging a 5-inch by 7-inch photo by a scale factor of xand mounting it on

a mat. You want the mat to be twice as wide as the enlarged photo and 2inches

less than twice as high as the enlarged photo.

Using Polyn om ials in Real Life

Write a model for the area of the mat around the photograph as a function of the

scale factor.

A =

= 140x220x35x2

SOLUTION

= 105x220x

A model for the area of the mat around the photograph as a function of the

scale factor xis A= 105x220x.

Algebraic

Model

5x

7x

14x

2

10x

Documents

Ch 8-5 Adding and Subtracting Polynomials