How would you factor this problem completely: 3x^2 yp^2 (2z -7) + 6x^2 ypz - 21x^2 yp - 6x^2 y(2z - 7) ?1?

Answer 1

3x^2 yp^2 (2z -7) + 6x^2 ypz - 21x^2 yp - 6x^2 y(2z - 7)
= 3x^2 y[p^2 (2z -7) + 2pz - 7p - 2(2z - 7)]
= 3x^2 y[(p^2-2) (2z -7) + (2z - 7)p]
= 3x^2 y(2z-7)[(p^2 + p - 2]
= 3x^2 y(2z-7)(p+2)(p-1)

Answer 2

I'm going to ignore the ?1? at the end of the question, because it doesn't seem to make any sense. So, here are the factoring steps I went through.

First, every term has an x^2, a y, and a multiple of 3. Let's take them out:

= 3(x^2)(y)( p^2(2z-7) +2pz - 7p - 6(2z-7) )

Next, there's a 2z-7 in the first term and the last term, and another one hiding in the middle two terms:

= 3(x^2)(y)( p^2(2z-7) +p(2z-7) - 6(2z-7) )
= 3(x^2)(y)(2z-7)(p^2 + p - 6)

Finally, the last quadratic form can be factored:

= 3(x^2)(y)(2z-7)(p+3)(p-2)

Answer 3

Let's see. You've got 4 terms here. Notice that every term has an x^2. They also have a "y". So you can factor both of those out:

3x²yp²(2z -7) + 6x²ypz - 21x²yp - 6x²y(2z - 7) =
x²y [ 3p²(2z-7) + 6pz - 21p - 6(2z-7) ]

All of the coefficients inside are factors of 3, so we can factor a 3 out too:

3x²y [ p²(2z-7) + 2pz - 7p - 2(2z-7) ]

Multiply out what's remaining inside:

3x²y [ 2p²z - 7p² + 2pz - 7p - 4z + 14 ]

There isn't a factor that's common to all the six terms inside, so the best you can do is combine some of them into small terms and factor out something from those. Get all the z's together and factor that z out:

3x²y [ 2p²z +2pz - 4z - 7p² - 7p + 14 ]
3x²y [ z(2p² +2p - 4) - 7p² - 7p + 14 ]
3x²y [ 2z(p² +p - 2) - 7p² - 7p + 14 ]

Notice we can factor out a -7 from the rest:

3x²y [ 2z(p² +p - 2) - 7(p² + p - 2) ]

Both of these inside terms have (p² + p - 2), which itself factors out to (p+2)(p-1). You can factor this out of each term, leaving:

3x²y(p+2)(p-1)(2z - 7)

Answer 4

3x^2 yp^2 (2z -7) + 6x^2 ypz - 21x^2 yp - 6x^2 y(2z - 7)
=(3x^2yp^2 -6x^2y)(2z-7) +3x^2yp(2z-7)
=(3x^2yp^2 -6x^2y +3x^2yp)(2z-7)
=3x^2y(p^2-2+p)(2z-7)
=3x^2y(p+2)(p-1)(2z-7)

Answer 5

= 3x^2y[p^2(2z-7)+2pz-7p-2(2z-7)]
= 3x^2y[p^2(2z-7)+p(2z-7)-2(2z-7)]
= 3x^2y(2z-7)[p^2+p+2]

Answer 6

i have no idea