Algebra 1--Step-by-Step

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Can someone show me how to solve these step-by-step? Please? Thank you.

Factor each polynomial by grouping. Check your answer.

1. 2r^2 - 6r + 12 - 4r
2. 14q^2 - 21q + 6 - 4q
3. w^3 -4w^2 + w - 4
4. 2p^3 - 6p^2 + 15 - 5p

  • Algebra 1--Step-by-Step -

    1.
    2r(r - 3) + 4(3 - r) , ahhh, did you notice that the brackets are opposite? , so ..
    = 2r(r-3) - 4(r - 3)
    = (r-3)(2r-4)

    Use the same "trick" on the others if you have to.

  • Algebra 1--Step-by-Step -

    My textbook says the answer is 2(r-2)(r-3), though.

  • Algebra 1--Step-by-Step -

    Surely you could see that 2 was an additional common factor contained in my (2r-4) factor.

  • Algebra 1--Step-by-Step -

    What? I don't understand what you mean.

  • Algebra 1--Step-by-Step -

    look at my answer ...

    (r-3)(2r-4)
    = (r-3)(2)(r-2)
    = 2(r-3)(r-2)

  • Algebra 1--Step-by-Step -

    Oh.

    My answers to the other equations:

    2. ?
    3. (w^2 + 1)(w - 4)
    4. (2p^2 - 5)(p - 3)

  • Algebra 1--Step-by-Step -

    2. (7q - 2)(2q - 3).

  • Algebra 1--Step-by-Step -

    3 and 4 are correct

    #2

    14q^2 - 21q + 6 - 4q
    = 7q(2q - 3) + 2(3-2q)
    = 7q(2q-3) - 2(2q-3)
    = (2q-3)(7q-2)

  • Algebra 1--Step-by-Step -

    Thank you.

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