Download Polynomial Expressions

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.