Refreshing Your Skills - 7

In Chapter 7, you will learn about polynomial functions and their graphs.

In this lesson you’ll review some of the terms and properties of polynomial expressions.

Expressions such as 3.2x, , 4x 3, and 2x0 are monomials.

234

x

More generally, the expression axn is a monomial when a is a real number and n is a nonnegative integer. A sum of monomials, like, is a polynomial.

You can add, subtract, multiply, and divide monomials and polynomials just as you can combine numbers.

3 234x + x  3.2x+2

4

Find the sum and difference of

and . 3 22x  6x  3x+ 9 3 24x   2x  x  2

3 2 3 2

3 3 2 2

3 2

2x  6x  3x+ 9 4x   2x  x  2

2x 4x  6x   2x  3x  x  9  2

6 4 4 11x x x

3 2 3 2

3 3 2 2

3 2

2x  6x  3x+ 9 4x   2x  x  2

2x 4x  6x   2x  3x+ x  9  2

2 8 2 7x x x

Hori

zonta

lly

Find the sum and difference of

and . 3 22x  6x  3x+ 9 3 24x   2x  x  2

3 2

3 2

3 2

2x  6x  3x+ 9

4x   2x  x  2

6 4 4 11x x x

3 2

3 2

3 2

2x  6x  3x+ 9

4x   2x  x  2

2 8 2 7x x x

Vert

ically

To multiply polynomials, it often helps to think of areas of rectangles.

In calculating the area of a rectangle, you multiply length times width.

If the sides of the rectangle are polynomial expressions, the area will also be a polynomial expression.

The area can be written as the product of the length and width, or as the sum of the areas of the interior regions.

Even though lengths and areas are not negative, you can use rectangle diagrams to represent individual terms and products.Copy each rectangle diagram and fill in the missing values to show the products and quotients of two polynomials.

Even though lengths and areas are not negative, you can use rectangle diagrams to represent individual terms and products.Write the two factors and the product for each diagram from the last part.