SOLUTION: Factor completely and show a detailed solution x^2r+1 + xy + 3x^2r z^3r + 3z^3ry

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Question 1040167: Factor completely and show a detailed solution
x^2r+1 + xy + 3x^2r z^3r + 3z^3ry

Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is solved below.
I am both Edwin and AnlytcPhil

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
           
You should not write:

x^2r+1 + xy + 3x^2r z^3r + 3z^3ry

because that translates as

x%5E2r%2B1+%2B+xy+%2B+3x%5E2r+z%5E3r+%2B+3z%5E3ry

which is not anything that will factor.

You must learn to use parentheses to show
what you mean when typing algebra all on
one line.  You should have this:

x^(2r+1)+xy+3x^(2r)z^(3r)+3z^(3r)y

for then it would be interpreted as this:

x%5E%282%2Ar%2B1%29%2Bx%2Ay%22%22%2B%22%223%2Ax%5E%282r%29%2Az%5E3r%2B3%2Az%5E%283r%29%2Ay


Factor x out of the first two terms:

x%28x%5E%282r%29%2By%29%22%22%2B%22%223x%5E%282r%29z%5E%283r%29%2B3z%5E%283r%29y

Factor 3z%5E%283r%29 out of the last two terms

x%28x%5E%282r%29%2By%29%22%22%2B%22%223z%5E%283r%29%28x%5E%282r%29%2By%29

Factor out %28x%5E%282r%29%2By%29

%28x%5E%282r%29%2By%29%28x%2B3z%5E%283r%29%29

Edwin