polynomials: solve x^2 - x - 6 < 0; prove (a + b)^3 = ...

[Sinful]

I just started Business Calculus and I'm already lost! Its been so long since I have done any of this and can't put it back in memory. I would be greatful if you could explain a couple things to me please. First

1) x^2 - x - 6 < 0

What are the steps to get it to the following stage?

(x - 3) (x + 2) < 0

I know it must be simple, but I just can't remember. I know -3 x 2 would equal 6, but does it matter which factor is in which parentheses?

My next question:

2) Prove that (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

I know (a + b)^2 = a^2 + 2ab + b^2, but how would I use this with the cubing?

Thanks in advance for the help!

 

[stapel]

1) This is called "factoring trinomials" or "factoring quadratics". There are many different cases and details, but you should be able to find many good lessons online (using the above search terms) to help you learn the various terms and techniques.

2) It might be better to learn how to multiply polynomials in general, rather than trying to memorize two or three formulas. (These formulas can be helpful, sure, but the general methodology will solve all problems, not just a few.)

To "use (a + b)²" to prove the cubing, note that (a + b)³ = (a + b)(a + b)(a + b) = (a + b)(a + b)². So multiply the expansion of (a + b)² by a + b to get the full expansion of the cube.

If you get stuck, please reply showing what you have tried. If you need links to lessons before you can get started, please specify the topics you seek.

Thank you.

Eliz.

 

[Sinful]

Thanks, I did a search and figured it out. I also went in for a tuitor session today..lol.


btw, how do I make the square on the computer rather than doing ^2 for it

 

[stapel]

how do I make the square on the computer rather than doing ^2 for it

You can use the LaTeX option (explained in articles listed in the "Forum Help" pull-down menu at the very top of the page).

Or you can use the HTML tags, where "x²" displays as "x²".

If you use the latter method (which is frequently simpler), just make sure that you do not have the "Disable HTML in this post" box ticked. :wink:

Eliz.