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algebra

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The first three equations I have solved, I would just appreciate someone checking them over to make sure I'm doing them right.
Find the GCF:
16x^2z ,40xz^2 , 72z^3
= 3^3z

Factor our GCF:
a(a+1) - 3(a+1)
= a+1

Factor Polynomial:
9a^2 - 64b^2
= (3a+8b)(3a-8b)

9w - w^3
= w(3) (?really unsure if correct?)

I'm not sure how to do the following, or where to even begin. Some help getting started would be very appreciated! :)

Factor Polynomials:
x^3y + 2x^2y^2 + xy^3

x^3 + ax + 3a + 3x^2

Factor:
18z + 45 +z^2

  • algebra -

    16x^2z ,40xz^2 , 72z^3
    the GCF I see is 4xz, I can't see how you got your answer.

    a(a+1) - 3(a+1)
    = (a+1)(a-3) fully factored

    9a^2 - 64b^2
    = (3a+8b)(3a-8b) that is ok

    9w - w^3 , I see a common factor of 3w
    = 3w(3 - w^2)

    x^3y + 2x^2y^2 + xy^3 first go for a common factor
    = xy(x^2 + 2xy + y^2)
    = xy(x+y)(x+y)
    = xy(x+y)^2

    x^3 + ax + 3a + 3x^2
    this is a "grouping" type of factoring
    = x^3 + 3x^2 + ax + 3a
    = x^2(x+3) + a(x+3)
    = (x+3)(a+3)

    18z + 45 +z^2
    = z^2 + 18z + 45
    = (z+15)(z+3)

  • algebra -

    in the first one: 16x^2z ,40xz^2 , 72z^3
    the only question I have is, how can it be 4xz when they don't all have the variable 'x'? the way I factored it was like this:
    16x^2z
    16 = 8 & 2 x^2z
    4&2 (x)(x)(z)
    2&2
    = 2^4

    40xz^2
    40 = 10 & 4 xz^2
    5&2 2&2 (x)(z)(z)
    = 5(2^3)

    72z^3
    72 = 36 & 2 z^3
    18&2 (z)(z)(z)
    9&2
    3&3
    = 3^2(2^3)

    with the answer being 2^3z, which is what they all have in common

  • algebra -

    3w-3

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