Reasoning/Method of choice
Give one appropriate factoring method you would choose for the quadratic x2 + 5x + 6, and briefly state why that method is efficient here.
What is Guess and Check! Because the leading coefficient is 1, and we know 2 and 3 multiply to 6 and add to 5.
Factor and find zeros for x2 - x - 6.
What is (x-3)(x+2), and x=3 and x=-2?
Given x3 +5x2 + 4x + 20, identify the factoring method you would use and write one sentence to justify it.
What is factor by grouping because you can factor out an x2 out of the first 2 terms and a 4 out of the second two terms to make them both equal x+5.
For 2x2 + 7x + 3, name a method you would use and give a one-sentence reason.
What is the AC method or the Slide and Divide method? Explanation: the leading coefficient is not 1.
Factor and find zeros for 2x2 - x - 6.
What is (2x+3)(x-2), and x=-3/2 and x=2.
For 5x2 + 6x + 1, pick a method and give a brief reason why that method is preferred
What is the use of slide-and-divide, because a≠1 and ac=5 have integer factor pairs 1 and 5, and 1+5=6.
For 3x2 - 2x - 8, which method would you prefer and why (one or two sentences)?
What is Grouping? Explanation: : multiply a*c = 3(-8) = -24. Find pair +4 and -6 (since 4 + (-6) = -2), split the middle term, and factor by grouping.
Factor and find zeros for 2x2 +12x + 10.
What is (2x+2)(x+5), and x=-1 and x=-5?
For x2+x−1, which method would you choose and why? Provide the zeros.
What is the quadratic formula, or completing the square, because the trinomial does not factor nicely with integers? Zeros:\frac{-1 \pm \sqrt{5}}{2} .
For x2 + 6x + 10, which factoring approach would you select and why?
What is completing the square or the quadratic formula? Explanation: Because we know the quadratic will have complex roots.
Factor and find zeros for 6x2 - 13x + 6.
What is (2x−3)(3x−2), and x=3/2, x=2/3?
For 4x2+9x+2, identify a what method you would use and explain why.
What is grouping? Because ac=8, find integers summing to 9 (1 and 8), split the middle term: 9x=8x+x, factor by grouping to get (4x+1)(x+2)(4x+1)(x+2). Zeros: x=−14, x=−2.
For 4x2 + 4x + 1, identify the best factoring method, explain your reasoning (include how you recognized the structure), and list the zeros.
What is the recognition of a perfect square trinomial or grouping? Explanation: varies, zeros x=-1/2 with multiplicity 2.
Factor and find zeros for 9x2 -30x + 25; explain your factoring choice and show zeros.
What is recognizing the perfect square trinomial or grouping? Factor: (3x-5)2, Zeros are x=5/3 with multiplicity 2.
Given 2x2−4x+5 identify the best strategy, fully justify it, and state the zeros.
What is the quadratic formula? Zeros: (1±isqrt.6)/2.