Honors Advanced Algebra Lesson 3-1

Warm-up Find the greatest common factor of the following. Factor it out of the expression x x x x x 2 – 16x + 4 Challenge: 12x 3 y – 15x 2 y xy 3

Refresher Find the greatest common factor for the following and and and 27 Challenge: 17 and 41

Greatest Common Factor of Polynomials When looking at polynomials, we must find the greatest common factor of both the coefficients and the variables. Example: 35x and 25x 2 Between 35 and 25, the greatest common factor is 5. Between x and x 2, the greatest common factor is x. Therefore, my greatest common factor is 5x; it is the highest number that will divide evenly into both 35x and 25x 2

Let’s Practice Find the greatest common factor of the following terms. 1. 3x and 9x 2. 16x 3 and 24x x and 42x 2 Challenge - 51x 5 and -68x 3

Factoring We use our knowledge of greatest common factors to factor out or simplify polynomial expressions. Example: Factor (4x 3 – 32x x) The greatest common factor is 4x. When we factor 4x out of each of our terms, we get the polynomial expression 4x(x 2 – 8x + 7) Distributing our greatest common factor back into the parentheses, we arrive at our original expression (4x 3 – 32x x)

Let’s Practice Factor the following expressions x 2 – 5x x 3 – 9x x + 18 Challenge: 18x 2 y + 24xy y 3

Rational Expressions A rational expression is a quotient of two polynomials. It is very important to remember that we cannot divide by 0 when working with rational expressions.

Example 1 Simplify 270x 3 y 2 365x 2 y 4

Example 2 Simplify. Factor Simplify

Example 3 Simplify

Example 4 Simplify

Let’s Practice Simplify the following 1. 18x x x 2 y4. 24xy 2

Let’s Practice Simplify the following: 1. 2.