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GreatestCommonFactor.notebook January 19, 2017 Please Do Now 1.19.17 1. Take your quiz on the Hub. 1 GreatestCommonFactor.notebook January 19, 2017 2 GreatestCommonFactor.notebook January 19, 2017 3 GreatestCommonFactor.notebook January 19, 2017 4 GreatestCommonFactor.notebook January 19, 2017 Greatest Common Factor In your own words, what is the definition of a Greatest Common Factor (GCF)? ~The largest factor shared by two or more numbers~ or ~The largest number that can be divided out of two or more numbers~ Example: What is the GCF of 16 and 48? What about 15, 45 and 21? 5 GreatestCommonFactor.notebook January 19, 2017 We can also factor out numbers and variables We must look for the things that the terms have in common. Ex. 1) Find the GCF of 5x and 25y Ex. 2) Find the GCF of 28x 2 and 42b Ex. 3) Find the GCF of 24x 3 and 8y 2 6 GreatestCommonFactor.notebook January 19, 2017 What is the GCF of 18x2 and 4y7 ? What is the GCF of 27x4 ,9x3 and 21x2 ? 7 GreatestCommonFactor.notebook January 19, 2017 with polynomials Let's begin with distributing. Multiply each of the following: a. 3(x + 2) b. 4(2x + 5) c. 10 (x2 +2x -1) d. 5x (x2 -2x + 4) Now, divide out what the terms have in common (FACTOR): a. 3x + 6 b. 8x + 20 c. 100x2 + 20x – 10 d. 5x3 -10x2 + 20x 8 GreatestCommonFactor.notebook January 19, 2017 with polynomials distribution *Taking out a GCF is just undoing the__________________________________. GCF *Before you factor a quadratic polynomial you must look for a ___________ to ensure “clean” factors. outside *The GCF does not “disappear”! It is just simply rearranged and set ____________ inside the parenthesis . the parenthesis, while the remaining terms go __________ 2 2 EX: 3x -15x + 2 -------------> 3(x – 5x + 6) 9 GreatestCommonFactor.notebook January 19, 2017 with polynomials Lets practice a few. Factor out the greatest common factor (GCF): a. 12x2 - 8x + 4 b. 10v2 + 30v + 60 c. -9c2 + 48c - 96 e. 3b2 +18b + 15 10 GreatestCommonFactor.notebook January 19, 2017 11 GreatestCommonFactor.notebook January 19, 2017 with polynomials 12 GreatestCommonFactor.notebook January 19, 2017 Application: Area of Shapes A video game pool has been scaled using variables so that it can zoom in and out safely. If the area is given by the expression 18a3 + 9a2 27a and the width is 9a, what is the programmed length of the pool? 9a 13
