Polynomials


 * Topic Overview**

Give the degree of the following polynomial: 2x5 – 5x3 – 10x + 9

This polynomial has four terms, including a fifth-degree term, a third-degree term, a first-degree term, and a constant term.

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To factor a polynomial you must find the **G**reatest **C**ommon **F**actor. The **GCF** is the greatest factor that divides evenly into each term. Finding the square of a binomial
 * Multiply each term in one binomial by each term of the other binomial. Drawing arrows as a visual reminder of what to do is a helpful technique.

Remember: Square the first term: x^2 Double (x)(-5): 2 * (-5x) = -10x Square the last term: (-5)^2 = 25 Write the sum of your three products: x^2 - 10x + 25
 * Square the first term.
 * Double the product of the two terms.
 * Square the last term.
 * Write the sum of your three products.

Finding the differences of two squares.

Remember: Square the first term. Square the last term. Write the differences of your first square and your second square. (3x - 2)(3x + 2) **1.Square the first term:** (3x)^2 = 9x^2 your first square and your second square:** 9x^2 - 4 +2 and +4 -2 and -4
 * Key Terms**
 * 2.Square the last term:** (2)^2 = 4
 * 3.Write the difference of
 * 4.Write factors of x^2, the first term of the trinomial, at the beginning of each set of parenthesis. Note that the coefficient of x^2 is 1.** (x )(x )
 * 5.List pairs of numbers that are factors of +8, which is the constant term of the trinomial. Choose the pair of factors that add to equal +6, the coefficient of the middle term of the trinomial.** +1 and +8 -1 and -8
 * 6.Write those two factors, with their sins, at the end of each set of parentheses.** (x + 2)(x + 4)

1.**(x + 7)(x + 2) **Foil the problem** x^2 + 2x + 7x + 14= x^2 + 9x + 14 **Solution**
 * Examples:

4.**
 * 2.**
 * 3.**
 * [[image:math_2.gif]]
 * [[image:math_3.gif]]

Word Problem:** a rectangular picture is three times as long as it is wide. the area of the picture is 588 inches^2. find the area of the picture. area=l*w 3x*x 3x^2=588 x^2=196 divide by 3 x=14 radical of both sides
 * Answer:**

w=14 l=42

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