# Polynomials: translate 'product of 3 less than twice x....'

#### Sarah1

##### New member
Hey, everyone. This is my first post here and after catching up on a bit of old material in preparation for my Math Placement test, I got stumped (as I always do) on a polynomial word problem. Here's how it goes:

Which of the following expression represents the product of 3 less than twice x and 2 more than the quantity 3 times x?

I know that the answer is 6x[sup:13pdxj5y]2[/sup:13pdxj5y] - 5x - 6, but I just don't know how and why. I haven't studied polynomials in years. I had it written out as: 3-x[sup:13pdxj5y]2[/sup:13pdxj5y]..then the rest sort of went beyond me.

Can someone explain how to translate the word problem into the polynomial and how to solve the polynomial?

Thank you so much for any help.

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: Polynomial Word Problem

Sarah1 said:
Hey, everyone. This is my first post here and after catching up on a bit of old material in preparation for my Math Placement test, I got stumped (as I always do) on a polynomial word problem. Here's how it goes:

Which of the following expression represents
Code:
the product of 3 less than twice x and 2 more than the quantity 3 times x?
-----------------       ------------------------------
( 2x - 3)                      (3x+2)

The statement above should be translated to

(2x - 3) * (3x + 2)

Now use FOIL to further expand it.
For a quick review, go to:

http://www.purplemath.com/modules/translat.htm

I know that the answer is 6x[sup:3emtoui7]2[/sup:3emtoui7] - 5x - 6, but I just don't know how and why. I haven't studied polynomials in years. I had it written out as: 3-x[sup:3emtoui7]2[/sup:3emtoui7]..then the rest sort of went beyond me.

Can someone explain how to translate the word problem into the polynomial and how to solve the polynomial?

Thank you so much for any help.

#### Sarah1

##### New member
That makes perfect sense now. Thanks so much!