factor polymials

Question

 

2x²y+4xy+6xy²

Answer 1

First, separate the terms into their factors (so that you can find common ones):

 

   2x²y          +       4 xy          +         6xy²

  2*x*x*y     +     2*2*x*y      +      2*3*x*y*y

 

Note that numbers have prime factors (or are themselves prime) and that, when you get experience with this, you can leave the smallest exponent of a variable.

 

Now, determine what factors are common and use the distributive principle:

  2*x*y(x      +       2             +       3*y)

 

Then, combine factors into numbers and variables with exponents (inside the parenthesis):

  2xy(x+2+3y)

 

 

Answer 2

While you're getting used to factoring polynomials, practice rewriting each term in the simplest factors you can.

 

Instead of 2x²y, write 2*x*x*y

4xy=2*2*x*y

6xy²=2*3*x*y*y

 

Once you have all the terms broken down into their factors, look the greatest common factor from each.

They all have a 2, but we can do better. They also all have an x and a y. We can factor out 2xy from every term in the expression. The convenience of rewriting each term is it makes it easier to see what's left after we factor. If I take out 2xy from each term, I'm left with x, 2, and 3y.

 

The factored expression should be 2xy(x+2+3y). You can check your work by re-distributing. Any questions?