# Ordering Polynomials

• Mar 7th 2006, 03:24 PM
greenstupor
Ordering Polynomials
I have a homework paper that's due tomorrow, and it has to be 100% correct to earn credit. I have everything correct except for two problems. My teacher said that the terms weren't in the correct order, but I have no idea what the correct order would be. I'd really appreciate some quick help.

1) \$\displaystyle (x - 2y)(3x^2 - 2xy + 6y^2)\$

My answer is: \$\displaystyle 3x^3 - 8x^2y + 16xy^2 - 12y^3\$

2) \$\displaystyle (2 - x)(3 - 4x)\$

My answer is: \$\displaystyle 4x^2 - 11x + 6\$

• Mar 7th 2006, 03:43 PM
Jameson
It's common to write from the highest power descending to the lower ones. You should write the powers of 3 first, then 2, etc.
• Mar 7th 2006, 04:39 PM
greenstupor
Quote:

Originally Posted by Jameson
It's common to write from the highest power descending to the lower ones. You should write the powers of 3 first, then 2, etc.

I actually did that the first time. My first answers were:

1) \$\displaystyle 3x^3 - 12y^3 - 8x^2y + 16xy^2\$

2) \$\displaystyle 4x^2 - 11x + 6\$

However, she marked those two wrong. On a related note, there was another, similar problem which I got correct.

3) \$\displaystyle (3x^2 - 5y^2)(2x - 4y)\$

My correct answer was: \$\displaystyle 6x^3 - 12x^2y - 10xy^2 + 20y^3\$

After seeing that problem 3 was correct, but problem 1 was wrong, I tried to reorder my terms in problem 1 in the same way as I did in problem 3 (\$\displaystyle x^3\$ first, then \$\displaystyle x^2y\$, then \$\displaystyle xy^2\$, then \$\displaystyle y^3\$). However, she still marked it wrong. So, I'm completely stuck. Any more tips?
• Mar 7th 2006, 05:01 PM
topsquark
Quote:

Originally Posted by greenstupor
I actually did that the first time. My first answers were:

1) \$\displaystyle 3x^3 - 12y^3 - 8x^2y + 16xy^2\$

2) \$\displaystyle 4x^2 - 11x + 6\$

However, she marked those two wrong. On a related note, there was another, similar problem which I got correct.

3) \$\displaystyle (3x^2 - 5y^2)(2x - 4y)\$

My correct answer was: \$\displaystyle 6x^3 - 12x^2y - 10xy^2 + 20y^3\$

After seeing that problem 3 was correct, but problem 1 was wrong, I tried to reorder my terms in problem 1 in the same way as I did in problem 3 (\$\displaystyle x^3\$ first, then \$\displaystyle x^2y\$, then \$\displaystyle xy^2\$, then \$\displaystyle y^3\$). However, she still marked it wrong. So, I'm completely stuck. Any more tips?

The ordering in your first answer is correct, the multiplication is wrong.

Generally when ordering, put the highest powers first, as you did. Typically you then "alphabetize" the answer by putting higher powers of a before b. For example if you have \$\displaystyle a^2c^3+6a^2b^3\$ you write \$\displaystyle 6a^2b^3+a^2c^3\$ because b comes before c. That's why your re-ordering is "more correct."

-Dan
• Mar 7th 2006, 05:12 PM
greenstupor
Thanks for the help. :)