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# March 20th, 2014

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### March 20th, 2014

1. 1. Polynomials Factoring Today: 1. Review 2. Factor x2 + bx + c trinomials
2. 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. 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. 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. 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. 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. 7. More Factoring Methods x3 - 18 - 3x2 + 6x 13x3 + 26x 4x2 – 20x + 25 (Perfect square trinomial) x2 + 25
8. 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. 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. 10. Class Work