Explain-how-you-can-use-the-distributive-property-to-check-the-binomial-factors-when-a-trinomial-has-been-factored-

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  1. Explain how you can use the distributive property to check the binomial factors when a trinomial has been factored. Include an example in your explanation.
  2. Explain how a polynomial with a GCF in all of the terms is factored differently from one without. Include an example in your explanation.
  3. Explain how a four-term polynomial is factored by grouping and when a quadratic trinomial can be factored using this method. Include examples in your explanation.
  4. Determine two different values of “b” in x2 + bx + 30 so that the expression can be factored into the product of two binomials.  Explain how you determined those values, and show each factorization.  Explain how your process would change if the expression was 2×2 + bx + 30.
  5. Bo factored x2 â€“ 10xy + 16y2 as follows: 
    Line 1 x2 â€“ 10xy + 16y2
    Line 2 x2 â€“ 8xy – 2xy + 16y2
    Line 3 x(x – 8) – 2y(x – 8y)
    Line 4 prime
    1. Did Bo correctly factor the polynomial? Justify your response by explaining why it is is factored correctly or by showing the correct solution if it is not factored correctly.
    2. Explain how you would know if a polynomial of the form ax2 + bxy + cy2was prime.
  6. Vicky factored 30×2 + 76x + 48 as follows:
    Line 1 30×2 + 76x + 48
    Line 2 30×2 + 36x + 40x + 48
    Line 3 6x(5x + 6) + 8(5x +6)
    Line 4 (6x + 8)(5x + 6)
    1. Did Vicky completely factor the polynomial? Justify your response by explaining why it is is factored completely or by showing the correct solution if it is not factored completely.
    2. Would the problem produce a different result if Line 2 was written as 30×2+ 40x + 36x + 48? Explain why or why not.

 
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