9x2+6x+1
--------------
1-9x2
2=squared
I have the answer just cant figure out how to write it. Been busting my brain on this one all night! Some Help would be Great!
2006-09-18 15:55:27 · 6 answers · asked by ahillworks 1 in Science & Mathematics ➔ Mathematics
answer is 3x+1 over 1-3x might help alittle.
2006-09-18 16:03:59 · update #1
9x^2+6x+1 3x+1
---------- = ------ How in deatail?
1-9x^2 1-3x
2006-09-18 16:16:03 · update #2
When factoring polynomials, all you can really use when doing it by hand is trial and error, meaning you have to test out all the possibilities that make sense (so try to start with the ones that make the most sense).
To factor the first polynomial, look at your possible choices, and try all of them. You know that you need two terms: (ax + b)(cx + d), where a, b, c, and d are numbers that, when plugged into the equation and you multiply that together, you end up with your original polynomial. (Any of them can equal any of the others.)
You know that the ax and cx terms when multiplied together must give you 9x^2. The only two combinations that will give you 9x^2 are (3x)(3x) and (9x)(x). Since 3x seems more logical (you need a 6x and a +1 term), start testing out those possibilities.
Next, you see that there's a 6x term in there. If 3x + 3x = 6x, you just need to add the two front terms together. So what can you put in for c and d to give you this 3x + 3x result? Remember, you can only get single x terms from multiplying your first term by the added term. (3x + c)(3x + d). C and d must equal 1 for you to get a 3x + 3x = 6x term in your answer. You get this by adding one to each term, so factoring the problem this way gives you (3x + 1)(3x + 1). Test it out and see that it gives you 9x^2 + 6x + 1.
Now that you have your numerator factored, it's time to factor the denominator.
1 - 9x^2
Whenever you have a perfect square subtracted from another perfect square, you can always factor them this way:
(a^2 - b^2) = (a - b)(a + b).
This means that
(1 - 9x^2) = (1 - 3x)(1 + 3x)
So now you put your numerator and denominator factors back into the problem:
(9x^2 + 6x + 1)
------------------- =
(1 - 9x^2)
(3x + 1)(3x + 1)
--------------------- =
(1 - 3x)(1 + 3x)
(3x + 1)(3x + 1) <--cancel the (3x + 1) term with bottom
---------------------
(1 - 3x)(3x + 1) <--cancel this (3x + 1) term
Notice that both the numerator and denominator have the term (1 + 3x). If you cancel out both these terms from the numerator and denominator, you have
(3x + 1)
----------
(1 - 3x)
2006-09-18 16:16:41 · answer #1 · answered by Dumblydore 3 · 1⤊ 0⤋
9x2+6x+1 Is a trinomial. If you are needed to factor it, it goes as follows.
(3x+1) (3x+1) or (3x+1)^2 That simple. Foil it back out to check your answer
3x * 3x = 9x2 F
3x * 1 = 3x O
1 * 3x = 3x I
1 * 1 = 1 L
9x2 +3x +3x +1 Collect like terms
9x2 + 6x + 1
There is your answer
2006-09-18 22:59:51 · answer #2 · answered by Eric 2 · 0⤊ 0⤋
you should factor the numerator and denominator
9x^2+6x+1 = (3x)^2+2*(3x)*1 + 1 = (3x+1)^2 (using (a+b)^2 formula
1-9x^2 = 1^2-(3x)^2 = (1+3x)(1-3x) (using a^2-b^2 = (a+b)(a-b)
so ratio = (3x+1)^2/((3x+1)(1-3x)) = (3x+1)/(1-3x)
cancelling 3x+1 from both numerator and denominator
2006-09-18 23:21:57 · answer #3 · answered by Mein Hoon Na 7 · 0⤊ 0⤋
First collapse the equation...
The numerator becomes (3x + 1)*(2X + 1) and the denominator becomes -(3x + 1)*(3x-1).
(3x + 1)*(2X + 1)
-----------------------
-(3x + 1)*(3x-1)
This reduces down to
-(2x + 1)
------------
(3x - 1)
2006-09-18 23:02:00 · answer #4 · answered by The Terminator 2 · 0⤊ 0⤋
(3x+1)^2
Sorry, I have no idea how to explain it. Just trial and error.
2006-09-18 22:59:06 · answer #5 · answered by something 3 · 0⤊ 0⤋
(3x + 1)^2
--------------------
(1 - 3x) (1 + 3x)
becomes
(1 + 3x)
----------
(1 - 3x)
2006-09-18 23:07:02 · answer #6 · answered by ali 6 · 0⤊ 0⤋