Create your own factorable polynomial with a GCF. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.?

3 Answers

• ?

  3 days ago

  4x^2 + 8x + 4

  4(x^2 + 2x + 1) – remove GCF of 4

  4(x + 1)(x + 1) – factor

  4(x + 1)^2 – collect like terms

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• Puzzling

  3 days ago

  One way is to work backwards.

  Start with a polynomial that isn’t factorable:

  3x + 5

  Then multiply it by a common factor — anything you like. I’m going to pick 7x²

  7x²(3x + 5)

  Then also expand it out by distributing:

  21x^3 + 35x²

  Form 1:

  21x^3 + 35x² – unfactored

  Form 2:

  7x²(3x + 5) – factored with GCF of 7x² brought to the front

  Update:

  You could also multiply two binomials and make a quadratic.

  Example:

  (7x + 2)(3x + 5)

  7x(3x + 5) + 2(3x + 5)

  = 21x² + 35x + 6x + 10

  = 21x² + 41x + 10

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• -j.

  3 days ago

  I don’t understand the question. “GCF” stands for greatest COMMON factor, and you can’t have a common factor unless you have at least two polynomials for the factor to be common to.

  Is part of the question missing?

  0