# Factor the Polynomials

Factor the polynomials using whatever strategy seems appropriate. State what methods you will use and then demonstrate the methods on your problems, explaining the process as you go. Discuss any particular challenges those particular polynomials posed for the factoring.Problem 52 Problem 7818z + 45 + z2 a4b + a2b3 For the problem on page 353 make sure you use the ac method regardless of what the books directions say. Show the steps of this method in your work in a similar manner as how the book shows it in examples.Problem 66 Incorporate the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work.):o Factoro GCFo Prime factorso Perfect squareo GroupingSince there are several different types of factoring problems assigned from pages 345-346, four types will be demonstrated here to offer a selection, even though individual students will only be working two from these pages.#73. x3 2?2 9x + 18 Four terms means start with groupingx2(x 2) 9(x 2) The common factor for each group is (x 2)(x 2)(x2 9) Notice the difference of squares in second group(x 2)(x 3)(x -+ 3) Now it is completely factored.#81. 6w2 12w 18 Every term has a GCF of 66(w2 2w 3) Common factor is removed, now have a trinomialNeed two numbers that add to -2 but multiply to -3Try with -3 and +16(w 3)(w + 1) This works, check by multiplying it back together#97. 8vw2 + 32vw + 32v Every term has a GCF of 8v8v(w2 + 4w + 4) The trinomial is in the form of a perfect square8v(w + 2)(w + 2) Showing the squared binomial8v(w + 2)2 Writing the square appropriately#103. -3y3 + 6y2 3y Every term has a GCF of -3y-3y(y2 2y + 1) Another perfect square trinomial-3y(y 1)(y 1) Showing the squared binomial-3y(y 1)2 Writing the square appropriatelyHere are two examples of problems similar to those assigned from page 353.5b2 13b + 6 a = 5 and c = 6, so ac = 5(6) = 30. The factor pairs of 30 are 1, 30 2, 15 3, 10 5,6-3(-10)=30 while -3+(-10)= -13 so replace -13b by -3b and -10b5b2 3b 10b + 6 Now factor by grouping.b(5b 3) 2(5b 3) The common binomial factor is (5b 3).(5b 3)( b 2) Check by multiplying it back together.3?2 + x 14 a = 3 and c = -14, so ac =3(-14)= -42. The factor pairs of 42 are1, -42 -1, 42 3, -14 -3, 14 2, -21 -2, 21 6, -7 -6, 7We see that -6(7) = -42 while -6 + 7 = 1 so replace x with -6x + 7x.3?2 6x + 7x 14 Factor by grouping.3x(x 2) + 7(x 2) The common binomial factor is (x 2).(x 2)(3x + 7) Check by multiplying it back together.CLICK HERE TO GET MORE ON THIS PAPER !!!

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