Topic 12 Factoring

# Find all the factors of 6x 3 solution the factors of

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Find all the factors of 6x 3 Solution: The factors of 6x 3 are 1,x,x 2 , x 3 and 2,2x,2x 2 ,2x 3 and 3,3x,3x 2 ,3x 3 and 6,6x,6x 2 ,6x 3 Example 8: Find all the factors of 4y 2 Solution: The factors of 4y 2 are 1,y,y 2 and 2,2y,2y 2 and 4,4y,4y 2 The greatest common factor (GCF) of two expressions is the largest factor they both share. There are two methods to finding the GCF of two expressions the first is by writing out all the factors of each expression and then finding the largest result that they both share. This method is very time consuming as the following worked example shows. Example 9: Find the GCF of 12x 3 and 16x 2 Solution: The factors of 12x 3 are 1 , x , x 2 , x 3 2,2x,2x 2 ,2x 3 3,3x,3x 2 ,3x 3 4,4x,4x 2 ,4x 3 6,6x,6x 2 ,6x 3 12,12x,12x 2 ,12x 3 The factors of 16x 2 are 1 , x , x 2 2,2x,2x 2 4,4x,4x 2 8,8x,8x 2 16,16x,16x 2 The common factors are 1,x,x 2 2,2x,2x 2 4,4x, 4x 2 The GCF of 12x 3 and 16x 2 is 4x 2 The second method for finding the GCF of two expressions is to find the GCF of the constants and the exponentials separately and then combine the result. Example 10: Find the GCF of 12x 3 and 16x 2 Solution: The GCF of 12 and 16 is 4 The GCF of x 2 and x 3 is x 2 (The smaller of the two powers) The GCF of 12x 2 and 16x 3 is 4x 2 Example 11: Find the GCF of 10y 4 x 2 and 25y 3 x 3 Solution: The GCF of 10 and 25 is 5 The GCF of x 2 and x 3 is x 2 (The smaller of the two powers) The GCF of y 4 and y 3 is y 3 (The smaller of the two powers) The GCF of 10y 4 x 2 and 25y 3 x 3 is 5x 2 y 3

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Olympic College Topic 12 Factorisation Page | 4 Exercise 1: 1. Find all the factors of the following numbers. (a) 26 (b) 60 (c) 82 (d) 144 (e) 100 2. Find all the factors of the following exponentials. (a) x 6 (b) x 4 (c) b 3 x 2 (d) c 2 d 2 (e) a 5 b 3. Find all the factors of the following expressions. (a) 6x 3 (b) 4b 4 (c) 20x 2 (d) 10d 3 (e) 12b 4. Find the greatest Common Factors GCF for each of the following. 5. Find the greatest Common Factors GCF for each of the following. 6. Find the greatest Common Factors GCF for each of the following.
Olympic College Topic 12 Factorisation Page | 5 2. Factoring by taking out a Common factors. When we expand parenthesis we can use the distributive law so that 5(2x 7) = 10x 35 Factorising an expression simplifies it by reversing the process of expanding parenthesis. So we take 10x 35 = 5(2x 7) this process is called factoring by taking out a common factor This process can be split into two steps.

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