# Introduction to Polynomials

### Learning Objectives

By the end of this section, you will be able to:- Identify the degree and leading coefficient of polynomials.
- Add and subtract polynomials.
- Multiply polynomials.
- Use FOIL to multiply binomials.
- Perform operations with polynomials of several variables.

**Figure 1**

[latex]\begin{array}{ccc}\hfill A& =& {s}^{2}\hfill \\ & =& {\left(2x\right)}^{2}\hfill \\ & =& 4{x}^{2}\hfill \end{array}[/latex]

Then find the area of the triangle in square feet.
[latex]\begin{array}{ccc}\hfill A& =& \frac{1}{2}bh\hfill \\ & =& \text{ }\frac{1}{2}\left(2x\right)\left(\frac{3}{2}\right)\hfill \\ & =& \text{ }\frac{3}{2}x\hfill \end{array}[/latex]

Next find the area of the rectangular door in square feet.
[latex]\begin{array}{ccc}\hfill A& =& lw\hfill \\ & =& x\cdot 1\hfill \\ \hfill & =& x\hfill \end{array}[/latex]

The area of the front of the doghouse can be found by adding the areas of the square and the triangle, and then subtracting the area of the rectangle. When we do this, we get [latex]4{x}^{2}+\frac{3}{2}x-x{\text{ft}}^{2}[/latex], or [latex]4{x}^{2}+\frac{1}{2}x[/latex] ft^{2}. In this section, we will examine expressions such as this one, which combine several variable terms.

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- College Algebra.
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