General Sign Patterns for Factoring TrinomialsDate: 04/12/2005 at 22:51:44 From: Chris Subject: Signs in Trinomials How can you tell whether the numbers should be negative or positive in trinomials? I just don't seem to get it. Can you help me? Date: 04/13/2005 at 10:40:55 From: Doctor Ian Subject: Re: Signs in Trinomials Hi Chris, You can tell by looking at the pattern. There are three possibilities: 1. (x + a)(x + b) Both added 2. (x + a)(x - b) One added, one subtracted 3. (x - a)(x - b) Both subtracted (Assume that a and b are both positive.) By expanding these, we can see that the pattern of signs in the quadratic tells us which one we're dealing with: 1. (x + a)(x + b) = x^2 + (a+b)x + ab 2. (x + a)(x - b) = x^2 + (a-b)x - ab 3. (x - a)(x - b) = x^2 - (a+b)x + ab So x^2 + __x + __ -> Case 1 x^2 - __x + __ -> Case 3 x^2 +/- __x - __ -> Case 2 In practice, I haven't actually memorized the pattern. What I do is look at the last sign, and if it's negative, I know that I have to have one added and one subtracted: ... - 3 -> (x + a)(x - b) Otherwise, I look at the second sign, and if it's negative, I know I have to have two subtractions: ... - 5 + ... -> (x - a)(x - b) Otherwise, I know I have two additions. Does this make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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