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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, 2x0 are monomials. 3 2 x 4 , 4x 3, and 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, 4x3+ 3 x2 3.2x+2 is a polynomial. 4 You can add, subtract, multiply, and divide monomials and polynomials just as you can combine numbers. Horizontally Find the sum and difference of 2x3 6x2 3x+9 2x 3 2 and 4x 2x x 2 . 2x3 6x2 3x+9 4x3 2x2 x 2 3 4x3 6x2 2x2 3x x 9 2 6 x 3 4 x 2 4 x 11 2x 2x3 6x2 3x+9 4x3 2x2 x 2 3 4x3 6x2 2x2 3x+ x 9 2 2 x 3 8 x 2 2 x 7 Vertically Find the sum and difference of 2x3 6x2 3x+9 3 and 4x3 2x2 x 2 . 2 2x 6x 3x+9 2x3 6x2 3x+9 4x 2x x 2 4x3 2x2 x 6 x 3 4x 2 4x 11 2x 3 8x 2 2x 7 3 2 2 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.