# Thread: Basic Operations with Polynomials

1. ## Basic Operations with Polynomials

Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?
A. –6x2 + 25x + 6
B. 6x2 + 5x + 6
C. 6x2 – 5x + 6
D. 6x2 – 5x – 6
E. 6x2 – 13x – 6

Please give an explanation on how to do this problem. Thanks!

2. Originally Posted by missbritt
Which of the following expressions represents the product of 3 less than twice x and 2 more than the quantity 3 times x ?
A. –6x2 + 25x + 6
B. 6x2 + 5x + 6
C. 6x2 – 5x + 6
D. 6x2 – 5x – 6
E. 6x2 – 13x – 6

Please give an explanation on how to do this problem. Thanks!
I think this is just an exercise in converting words into math equations.

The question is asking for a product, so you know you will have to multiply some factors together. So you could mentally in your head think
a * b, a basic way to get a product, right?

Then after the word "of", that's telling you what the factors of the product are. There's an "and" in between, so that is separating the factors, In this case it looks like only 2 are being described.

Factor 1 is "3 less than twice x"
Factor 2 is "2 more than the quantity 3 times x"

The word "quantity" in factor 2 tells you that it will have some kind of compound operations.

For factor 1, "twice x" is 2x, and "3 less than" this would be 2x - 3

For factor 2, we have a "quantity" which is "3 times x", which is 3x. And we have "2 more than" this quantity, which would be 3x + 2.

Those are the two factors of the product. Multiplying them together:

(2x - 3) (3x + 2).

Now you multiply them together using FOIL and compare the answer you get to the 4 answers above. One of them should match.

3. Thanks a billion. That's exactly what I needed to know.