Help In College Algebra (rudimentry stuff)

[Randerolf]

Hey guys! I've really learned a lot so far from the links that you've given me. thank you very much! I'm still having few troubles with some promblems that I need to understand for my test

Answers are on bottom. I worked some out as much as I could.

Thank you for your help!

Question 1 - Factor each polynomial

20z2 + 18x2 – 8zx – 45zx
_____________________________________________________________
Question 2 – Simplify the rational expression by reducing to lowest terms.

8x3 – 27_____
8x2 – 14x + 3

Next __ ?___________
(4x - ?)(2x- ? )

__________________________________________________________________
Question 3 – Simplify the following rational expressions by performing the indicated operations. Write answer in lowest terms:

2m² – 5m +12 ÷ 4m² - 9________
m ² - 10m + 24 m ² - 9m +18

Next (2m+?) (m-?) ÷ (2m + 3)(2m-3)
(m-4)(m-6) (m -6)(m-3)
________________________________________________________
Question 4 – Divide:
2x ² - 4x + 5
3x – 2
________________________________________________________
Question 5 – Expand:

(4x ³ - 3y²)4


ANSWERS

1 – (2x-5z)(9x-4z)
2-
4x2 +6x +9
4x -1
3 -
m-3
2m-3

4-
2x – 8 + 29___
3 9 27x - 18

("two over three times X minus eight over nine plus 29 over 27x minus 18")

5- 256x12 – 768x9y2 +864x6y4 – 432x3y6 + 81y8

[JadziaDax]

First, let me start by saying if you want to express "x squared", please don't type x2. That would be represented as x^2 (x to the second power).

Now...

Originally posted by Randerolf
[B][b]Question 1 - Factor each polynomial

20z2 + 18x2 – 8zx – 45zx

if this really reads as 20z^2 + 18x^2 - 8zx - 45zx, then the first thing you do is combine like terms (the - 8zx and the - 45zx). This would then give you the expression 20z^2 - 53zx +18x^2. This new expression I hope you can factor with no problems.

Question 2 – Simplify the rational expression by reducing to lowest terms.

8x3 – 27_____
8x2 – 14x + 3

Next __ ?___________
(4x - ?)(2x- ? )

trying to make fractions in text is not working for my eyes (especially when I hit "quote" and see a bunch of mess...)
But I think you were trying to say:

(8x^3 - 27) / (8x^2 - 14x + 3)

The numerator is the difference of cubes (both terms are a perfect cube and one is being subtracted from the other). And the difference of cubes can be factored as A^3 - B^3 = (A - B)(A^2 + AB + B^2). The denominator is also factorable. After you factor both numerator and denominator, you will see that something will cancel.


Start with those. And I'll get back to you on the rest.

[JadziaDax]

Originally posted by Randerolf
[B]Question 3 – Simplify the following rational expressions by performing the indicated operations. Write answer in lowest terms:

2m² – 5m +12 ÷ 4m² - 9________
m ² - 10m + 24 m ² - 9m +18

Next (2m+?) (m-?) ÷ (2m + 3)(2m-3)
(m-4)(m-6) (m -6)(m-3)

Remember that if you are dividing by a fraction, you flip the second and multiply.

Just finish your factoring (I wont factor for you).

Question 4 – Divide:
2x ² - 4x + 5
3x – 2

Is this supposed to be long division? If so, it's too much for me to type out right now... so take a look at http://www.sosmath.com/algebra/factor/fac01/fac01.html
All you ever needed to know about polynomial long division, but were afraid to ask.

Question 5 – Expand:

(4x ³ - 3y²)4

You can expand this yourself by just thinking of it as (4x^3 - 3y^2)^2 * (4x^3 - 3y^2)^2 (in other words, (4x^3 - 3y^2)^2 times itself). That makes it easier to do by hand if you have to show work. The shortcut method to doing this is called "binomial expansion". By using Pascal's Triangle, you can arrive at your answer a lot faster. See the article at http://www.geocities.com/thesciencef.../triangle.html for more help.