Lesson8 - The textbook exclusively uses the trial-and-error...

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1 MA 15200 Lesson 8 Section P.5 (part 2) To factor a trinomial of the form , 2 c bx ax + + using the ‘trial-and-error’ process. Follow these steps: 1. Make your first terms have a product of 2 ax . 2. Make your last terms have a product of c . 3. Find the sum of the inner and outer terms and check if it equals bx . If not, go back to steps 1 and 2 and try a different combination, until step 3 checks. Other students like to use grouping to factor a trinomial. Here are the steps for grouping. I sometimes call this the product/sum method. Follow these steps if the leading coefficient is not a 1: 1. If the trinomial is in the form c bx ax + + 2 , find a pair of numbers whose product is ac and whose sum is b . Call these numbers r and s . 2. Write the polynomial of the form c sx rx ax + + + 2 . Use the ‘grouping’ method to factor. a) Group the first two terms together and factor out a GCF. b) Group the last two terms together and factor out a GCF. c) Now factor out the GCF of the polynomial. Use whichever method is best for you!
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Unformatted text preview: The textbook exclusively uses the trial-and-error method. Most students have greater success if they sometimes use the product/sum method. Ex 1 : Factor each completely. 2 2 2 ) 9 68 32 ) 10 17 6 a y y b x xy y--=-+ = 2 2 2 4 3 2 2 ) 6 47 35 ) 6 11 35 ) 81 72 16 c m mn n d w w w e r r-+-=--= + + When given a polynomial to factor, this is the order you should follow. 1. Always look for a GCF first. 2. If the polynomial has two terms (binomial), see if it is a difference of squares. 3. If the polynomial has 4 terms, try the grouping method. 4. If the polynomial has 3 terms (trinomial), see if it is a perfect square trinomial. 5. If a trinomial is not a perfect square, try trial-and-error or the grouping method. Ex 3: Factor each polynomial completely, if possible. 3 2 5 ) 3 4 12 ) 3 48 a a a a b n n +---3 2 ) 4 32 64 c r r r-+ 3 6 4 2 3 2 3 2 ) 4 12 ) 2 32 16 ) 5 6 d n n n e x x x g g g g---+---4 3 2 ) 12 9 30 h x x x--...
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This note was uploaded on 01/18/2012 for the course MATH 152 taught by Professor staff during the Fall '09 term at Purdue University-West Lafayette.

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Lesson8 - The textbook exclusively uses the trial-and-error...

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