Algebra

Iwill post an example of # 3 and instructions for the ac method at thebottomForproblems 1 and 2 factor the polynomials using whatever strategyseems appropriate. State what methods you will use and thendemonstrate the methods on your problems, explaining the process asyou go. Discuss any particular challenges those particularpolynomials posed for the factoringForproblem 3 make sure you use the “ac method”, Show the steps ofthis method in your work in a similar manner of the example.Incorporatethe following five math vocabulary words into your discussion. Useboldfonttoemphasize the words in your writing (Donot write definitions for the words; use them appropriately insentences describing your math work.FactorGCFPrimefactorsPerfectsquareGrouping b^3 + 49b               (Factoring completely) a^2 + 7ab 10b^2    (Factoring with Two Variables) 3a^2-14a +15         (Factor each trinomial using the ac method. Instructions for this method are                                    below)Theac MethodThefirst step in factoring ax^2 + bx + c with a =1 is to find twonumbers with a product of c and a sum of b. If a cancels out 1, thenthe first step is to find two numbers with a product of ac and a sumof b. This method is called the ac method. The strategy for factoringby the ac method follows. Note that this strategy works whether ornot the leading coefficient is 1. Howto factor the trinomial ax^2 + bx + c:  Find two numbers that have a product equal to ac and a sum equal tob. Replace bx by the sum of two terms whose coefficients are the twonumbers found in (1). Factor the resulting four-term polynomial by grouping.Hereis an example of #35b^2– 13b + 6                a = 5 and c = 6, so ac = 5(6) = 30.                                        The factorpairs of 30 are 1 and 30, 2 and 15, 3 and 10, 5 and 6                                        -3(-10)=30 while -3+(-10)= -13 so replace -13b by -3b and -10b 5b^2– 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