Quick Algebra help

[Nocturnal]

Rewrite each multiplication problem as a division problem. There is more than one correct answer.

(x + 3)(x + 1) = 2x^2 + 5x + 3

How the hell do you rewrite it as a division problem?

I need to divide polynomials.

 

[Nocturnal]

So in my answer book it says to put the answer over the (x + 3) can anyone tell me why they do this? Or why that is the proper way?

 

[Legendary]

((2x^2 + 5x + 3) / (x^2 + 4x + 3)) - 1 = 0

 

[Nocturnal]

Originally posted by: Legendary
((2x^2 + 5x + 3) / (x^2 + 4x + 3)) - 1 = 0

This if for dividing polynomials by binomials etc.

 

[imported_Papi]

what is algebra actually used for?

 

[TMTCC]

Well if you factor 2x^2 + 5x + 3, you get (2x + 3)(x + 1), and then you can cancel out (x + 1) from both sides. You're left with (x+3)/(2x+3) = 1 if you then divide both sides by (2x + 3)

 

[Nocturnal]

Originally posted by: TMTCC
Well if you factor 2x^2 + 5x + 3, you get (2x + 3)(x + 1), and then you can cancel out (x + 1) from both sides. You're left with (x+3)/(2x+3) = 1 if you then divide both sides by (2x + 3)

How do you go about factoring 2x^2 + 5x + 3 anyway? That is the part I'm confused About.

 

[TMTCC]

Factoring is just one of those things you just "see" after doing a lot of problems. There's no "step by step" method per say, but basically I look at the 2x^2 and 3, and then I try to think of ways of combining them to bet the 5x in the middle. Of course, 2x^2 can be broken into 2x times x, and 3 is broken into 3 times 1. I see that I can multiply 3 by x, resulting in 3x, leaving 1 times 2x. Add them together, and you get 5x! You just need to do a couple of problems to get the hang of factoring.

 

[Nocturnal]

Originally posted by: TMTCC
Factoring is just one of those things you just "see" after doing a lot of problems. There's no "step by step" method per say, but basically I look at the 2x^2 and 3, and then I try to think of ways of combining them to bet the 5x in the middle. Of course, 2x^2 can be broken into 2x times x, and 3 is broken into 3 times 1. I see that I can multiply 3 by x, resulting in 3x, leaving 1 times 2x. Add them together, and you get 5x! You just need to do a couple of problems to get the hang of factoring.

Thanks, I guess with time I'll start to get it. I'm in an environment right now in which I have many distractions going on at once. I'm usually at my school's cafeteria but today I'm at home because I needed to do some things online. Of course having the internet near is not the greatest study tool available. Thanks again.