Factoring - Factoring Notes Math 117 I have been asked to...

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Factoring Notes Math 117 I have been asked to explain how and when you know to factor. I will be taking problems from the text in chapter 5. When I teach this in a lecture format, I provide my students with a checklist to follow. When factoring, look for the following: 1) Always look to see if there is a common factor to take out. If there, is, take it out and continue factoring what is left if possible. Example 1-a Factor x 9 y 6 – x 7 y 5 – x 4 y 4 – x 3 y 3 Looking at this problem, I see that I have an x 3 and a y 3 common. When dealing with exponents, I always take the smallest one if each terms has that variable. X 3 y 3 (x 6 y 3 – x 4 y 2 – xy – 1) At this point, we could try to factor what is left in the parentheses, but it will not factor. Example 1-b 2x 2 – 2x – 8 We have a 2 in common with each term so we factor that out. 2(x 2 – x – 4) Again, we look to see if the middle is factorable, but it is not. So this is our answer. 2) If the problem has two terms, look for a difference of squares. Example 2a: 16x 2 – 25y 2 This is a difference of squares because it is subtraction and the terms are perfect squares. I.e. 16x 2 = (4x) 2 and 25y 2 = (5y) 2 So this factors to (4x + 5y)(4x – 5y) Example 2b: 24x 2 – 54 At first glance, this may not look like a difference of squares, but remember step 1. We need to factor our the common factor here which is 6. So we have 6(4x 2 – 9) Now the 4x 2 – 9 is factorable to 2x – 3 and 2x + 3 So our answer is 6(2x+3)(2x-3) 3) If we have three terms of the form x 2 + bx + c, we have a leading coefficient of 1. Remember the leading coefficient is the number with the first term (1x
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Factoring - Factoring Notes Math 117 I have been asked to...

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