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# March 20th, 2014

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• 1. Polynomials Factoring Today: 1. Review 2. Factor x2 + bx + c trinomials
• 2. Instead of simply memorizing rules & formulas, it really2 helps to understand why (for what purpose), you are adding, subtracting, factoring, etc. Remember, terms are separated by + or – signs. (The terms are all being added or subtracted). An example is: 10x2 + 15x Factoring is finding an equal expression that is a product, that is, the factors are multiplied. How do we factor 10x2 + 15x ??? The first step is to always look for a common factor. Is there one for this polynomial?We factor out the GCF of 5x. What remains is (2x + 3). The full factor is 5x(2x + 3). 10x2 + 15x = 5x(2x + 3) We multiply factors to find the terms of a polynomial. (These terms are either being added or subtracted.) The Main Idea
• 3. Steps to Factoring Completely: 1. Look for the GCF 2. Look for special cases. a. difference of two squares, b. perfect square trinomial 3. If a trinomial is not a perfect square, look for two different binomial factors. coming soon.. 4. If a polynomial has 4 terms, you can try to factor by grouping. 6. Not all polynomials can be factored. ...today 5. Understand what you are working with before you attempt to factor.
• 4. Products...Special A) Always be on the lookout for them B) Be able to recognize them in both factored and trinomial form 9x2 - 16x2 Factor these difference of squares: 18y3 – 8y 4m2 – 49n2 = (2m)2 – (7n)2 Difference of squares (2m + 7n)(2m – 7m)
• 5. FOIL With a Positive and a Negative (x + 3)(x - 5) F= (x•x) = x2 O= (x•-5) -5x I= (3•x) +3x L= (3•5) 15 Answer: x2 - 2x - 15 The larger number is negative, so the middle term is negative.
• 6. (x - 3)(x + 5) FOIL With a Negative and a Positive The opposite of our first example. The larger number is positive, resulting in a positive middle term. Answer: x2 + 2x - 15 ...But I thought if the signs were different, the middle term was cancelled out? This is true, but only if the two numbers are the same! (3x + 5)(3x – 5)
• 7. More Factoring Methods x3 - 18 - 3x2 + 6x 13x3 + 26x 4x2 – 20x + 25 (Perfect square trinomial) x2 + 25
• 8. To solve these, we use FOIL in reverse. x2 + x – 6 = (x ) ( x ) Check the signs: Then, list all the factors of the last term, looking for the sum of the middle term, and the product of the last term. Factoring Trinomials: (1x2 + bx + c) (The leading coefficient is always 1) x2 + x – 6 = x2 + x – 6 =6 1,6 2,3 (x + )(x - ) (x + 3)(x - 2 ) No algebra magic or wizardry here. Factor and check for the correct fit.
• 9. Factor the polynomial x2 + 13x + 30. That was too easy, one moreFactor the polynomial x2 – 2x – 35. Since our two numbers must have a product of – 35 and a sum of – 2, the two numbers will have to have different signs. Factors of – 35 Sum of Factors – 1, 35 34 1, – 35 – 34 – 5, 7 2 5, – 7 – 2 Absolutely the last practice problem. 2ab2 – 26ab – 60a
• 10. Class Work