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Please help

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Name: FACTORING BY GROUPING COMMON CORE ALGEBRA II Ori You now have essentially three types of factoring: (1) greatest common factor, (2) difference of perfect squares, and (3) trinomials. We can combine gcf factoring with the other two to completely factor quadratic expressions. Today we will introduce a new type of factoring known as factoring by grouping. This technique requires you to see structure in expressions. (c) (x+5)(x-7)+(x-7)(x+1) Exercise #1: Factor a binomial common factor out of each of the following expressions. Write your final expression as the product of two binomials. (a) x (2x+1)+7(2x+1) (b) 5x(x−2)−4(x−2) Date: Exercise #2: Write the expression (x+3)(x-4)+5(x+3) as the equivalent product of binomials. Test this equivalency with x = 2 (d) (2x+8) (x+4)=(x-2)(x+4) Some very special polynomials can be factored by taking advantage of the structure we have seen in the last two problems. The key is to do mindful manipulations of expressions so that they remain equivalent but are written as an overall product. = 2x²(x-3)+5(x-3) Exercise #3: Consider the expression 2x² - 6x² +5x-15. Justify each step below with one of the three major properties of real numbers, i.e. the commutative, associative, or distributive. 2x³-6x² +5x-15=(2x³-6x²)+(5x-15) =(x-3)(2x²+5) COMMON COR GEBRA II, UNIT I MarkON -FUNCTIONS AND THEIR ALGERRA— -- 1957 2015
A step up from the last exercise occurs when the leading coefficient isn't one but is still a prime number. This is very often the case and makes at least part of the guessing much easier. Exercise #3: Using a guess-and-check technique, factor each of the following trinomials that have prime leading coefficients. Show each guess and its check. (a) 3x² +19x-40 (b) 2x² -15x+18 Finally, the hardest trinomials to factor are those whose leading coefficients are not prime. This is due to the fact that there are so many more intelligent guesses. In future lessons we will develop ways to eliminate some of these, but for now, the key will be to just keep guessing until you get it right. Exercise #4: Factor each of the following trinomials. Show each guess and its check. (a) 15x² +13x+2 (b) 10x² +13x-30 (c) 12x² +8x-15 (d) 36x²-35x+6 COMMON CORE ALCERS, IL UNIT " QUADRATIC FUNCHIENS AND THEIR ALGEBRA — LESSON #3 MATHINSTRUCTION, RED HOOK, NY 12574, © 2015
Name: FACTORING TRINOMIALS COMMON CORE ALGEBRA II HOMEWORK FLUENCY 1. Multiply each of the following binomial pairs and express your answer in simplest trinomial form. (a) (2x+5)(3x-2) (b) (3x-8)(5x-1) (c) (8x+3)(x+7) (d) (7x-5)(5x+2) 2. Which of the following is the correct factorization of the trinomial 12x²-23x+10? Hint - eliminate two of the choices because they are "unintelligent" guesses. (1) (6x-1)(3x-10) (3) (4x-5)(3x+2) (2) (6x-2)(2x-5) (4) (4x-5)(3x-2) (e) x²-5x+6 3. Written in factored form x² +16x-36 is equivalent to (1) (x-3)(x+12) (3) (x-2)(x+18) (2) (x-6)(x+6) (4) (x-9)(x+4) 4. Write each of the following trinomials in its factored form. These are the easiest trinomials to factor because the leading coefficient is equal to one. (a) x²-7x-18 (b) x² +14x+24 Date: (f) x²-15x+44 (c) x²-17x+30 (g) x² +21x+20 (d) x²-5x-6 (h) x²-6x-16 COMMON CORE Algebra II Unit #6 QUAMATIC FUNCTIONS AND THEIR ALGEBRA-LESSON #3 eMATHINSTRUCHON, RED HOOK, NY 12371, 0-2045
5. Each of the following trinomials has a leading coefficient that is prime. Using a guess-and-check technique, write each trinomial in its factored form. Show each guess and its check. (a) 5x²-41x+8 (b) 3x² + 4x-20 (c) 2x² -29x-15 (d) 7x² +39x+20 6. Each of the following trinomials has a non-prime leading coefficient. Using a guess-and-check technique, write each trinomial in its factored form. Show each guess and its check. (a) 18x²-25x+8 (b) 20x²-11x-42 REASONING 7. Consider the trinomial 12x² +7x-10. (a) Does this trinomial have a greatest common factor that could be "factored out"? (b) Why is (4x-2)(3x+5) not an intelligent guess for factoring this trinomial even though 4.3 12 and -2-5=-10? Consider your answer to part (a). COMMON CORE ÁLGEBRA IL UNIT #0–QUADRATIC PESSONS AND LILEHR -~~EBRA – LESSON #3 HUT HOOK NY 12571, C