Math Help: factoring, dividing poly's, simplifying, etc.

Paris

New member
Joined
Nov 25, 2006
Messages
4
1) Factor out the greatest common factor:

. . .3x^6 - 24x^5 + 18x^4

What I got was is:

. . .3x^4(x^2 - 8x + 6)

Did I do that right?

2) Divide and write the answer without exponents:

. . .(4 * 10^5) / (2 * 10^(-2))

I have no clue what to do.

3) Use the exponent rule to simplify the expression. Assume the variables represent nonzero real numbers.

. . .[(m^8 n)^(-2)] / [m^(-4) n^7]

I don't know what to do for this one.

4) Perform the indicated operation, and simplify your answer:

. . .[(x^2 - 3x - 18) / (x^2 - 6x + 9)] / [(x - 6) / (x - 3)]

Again...I don't know what to do.
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,789
1) Let's see

3/3 = 1
24/3 = 8
18/3 = 6
6-4 = 2
5-4 = 1
4-4=0

Perfect. This leads me to believe that you have more clue than you are suggesting on the others.

Helpful Pieces:

4/2 = 2
10^5 / 10^(-2) = 10^(5-(-2)) = 10^(5+2) = 10^7 = 10*10*10*10*10*10*10
 

stapel

Super Moderator
Staff member
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Feb 4, 2004
Messages
15,943
We can't teach lessons within this environment, so it would help if you could narrow down just where you're having difficulty. Since this content must have been covered in class and in your textbook, you must have some idea what to do. What have you tried? Where are you stuck?

1) This factoring is correct.

2) What is 4 / 2? (This is just grade-school division.) What is 10<sup>5</sup> / 10<sup>-2</sup>? (This is just a simple application of the exponent rules you learned.)

3) "What to do" is follow the instructions by applying the exponent rules you've learned, namely:

. . . . .x<sup>m</sup>x<sup>n</sup> = x<sup>m+n</sup>

. . . . .x<sup>m</sup> / x<sup>n</sup> = x<sup>m-n</sup>

. . . . .(x<sup>m</sup>)<sup>n</sup> = x<sup>mn</sup>

4) To handle the division by a fraction, do what you learned back in grammar school: flip the second fraction, and convert the division to multiplication. To simplify the multiplication, first cancel off any common factors. To do this, factor the quadratics by whatever method they taught you in class.

If you get stuck, please reply showing what you have tried and how far you have gotten. Thank you.

Eliz.
 

soroban

Elite Member
Joined
Jan 28, 2005
Messages
5,588
Hello, Paris!

1) Factor out the greatest common factor: .\(\displaystyle 3x^6 \,-\,24x^5\,+\,18x^4\)

What I got was: .\(\displaystyle 3x^4(x^2\,-\,8x\,+\,6)\;\;\)Did I do that right? . . . Yes!
2) Divide and write the answer without exponents: .\(\displaystyle \L\frac{4\cdot10^5}{2\cdot10^{-2}}\)

We have: \(\displaystyle \L\:\frac{4}{2}\,\cdot\,\frac{10^5}{10^{-2}}\)\(\displaystyle \;= \;2\,\cdot\,10^7\;=\;20,000,000\)


3) Use the exponent rules to simplify the expression: .\(\displaystyle \L\frac{(m^8n)^{-2}}{m^{-4}n^7}\)

We have: \(\displaystyle \L\:\frac{(m^8)^{-2}(n)^{-2}}{m^4n^7} \:=\:\frac{m^{-16}n^{-2}}{m^4n^7} \:=\:\frac{1}{m^{20}n^9}\)



4) Perform the indicated operation, and simplify your answer:
. . \(\displaystyle \L\frac{x^2\,-\,3x\,-\,18}{x^2\,-\,6x\,+\,9}\,\div\,\frac{x\,-\,6}{x\,-\,3}\)

To divide by a fraction, invert the second fraction and multiply.

We have: \(\displaystyle \L\:\frac{x^2\,-\,3x\,-\,18}{x^2\,-\,6x\,+\,9}\,\cdot\,\frac{x\,-\,3}{x\,-\,6}\)

Factor: \(\displaystyle \L\:\frac{(x\,+\,3)(x\,-\,6)}{(x\,-\,3)(x\,-\,3)}\,\cdot\,\frac{x\,-\,3}{x\,-\,6}\)

Reduce: \(\displaystyle \L\:\frac{(x\,+\,3)(\sout{x\,-\,6})}{(x\,-\,3)(\sout{x\,-\,3})}\,\cdot\,\frac{\sout{x\,-\,3}}{\sout{x\,-\,6}} \;=\;\frac{x\,+\,3}{x\,-\,3}\)

 

Paris

New member
Joined
Nov 25, 2006
Messages
4
Thank you everyone.
 
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