# DIVIDE: 2x^2-6y^2+3z^2-xy+7yz-7xz by x-2y+3z

vaaruni | Student

x-2y+3z)2x^2 - 6y^2 + 3z^2 - xy - 7yz - 7xz(2x + 3y - 13z

2x^2                       -4xy          +6xz

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0 + 3xy - 13xz - 6y^2 + 7yz + 3z^2

+3xy            - 6y^2  + 9yz

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0 + 0   - 13xz - 2yz   + 3z^2

- 13xz + 26yz - 39z^2

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0  + 0 + 0     - 28yz + 39z^2

joshmrusso | Student

You can do this problem as long division.

(2x^2-6y^2+3z^2-xy+7yz-7xz)/(x-2y+3z)

I'll try to make the notation as simple as possible here.

(x-2y+3z) | (2x^2-6y^2+3z^2-xy+7yz-7xz)
-(2x^2                  -4xy      +6xz) {multiply divisor by 2x}
-6y^2+3z^2+3xy+7yz-13xz
-(-6y^2          +3xy+9yz)      {multiply divisor by 3y}
3z^2          -2yz-13xz
-(-39z^2      +26yz-13xz) {*divisor by -13z}
42z^2      -28yz            {remainder}

Or 2x+3y-13z with a remainder of 42z^2-28yz

chandramohan | Student

x-2y+3z)2x^2-6y^2+3z^2-  xy+ 7yz-7xz(2x+3y+z

2x^2                  -4xy+      +6xz

0   -6y^2+3z^2+3xy+ 7yz-13xz

-6y^2         +3xy+9yz

0    +3z^2+0-2yz-13xz

3z^2    -2yz+xz

0               -13xz