Problem Set Suggestions

doughishere

Junior Member
Joined
Dec 18, 2015
Messages
59
I want to work on my more advanced factoring (its probably not more advanced). Anyone have any suggestions on problem sets that are similar to e) and f)?


Just like 30-40 that are similar or any really.



TIA!
 

Attachments

  • Capture.JPG
    Capture.JPG
    13.5 KB · Views: 1
Last edited:
There are many odd things about how math is taught. I am not sure that there are many real-world problems that require factoring. Factoring is usually a convenience rather than a necessity. And if finding a factoring takes a lot of time, then it is not even a convenience. Frequently (but not always) a common factor in each term provides the clue if there is a simple factorization. (There is no guarantee that there is any factorization of an expression unless it is a polynomial, and there is no guarantee that the factoring will be simple even if the expression is factorable.)

Let's start with \(\displaystyle x^3y - 4xy.\)

It should be obvious that both x and y are factors of every term. So

\(\displaystyle x^3y - 4xy = xy(x^2 - 4).\) Now you should see a difference of like powers.

\(\displaystyle x^3y - 4xy = xy(x^2 - 4) = xy(x - 2)(x + 2).\)

\(\displaystyle 3x^{3/2} - 9x^{1/2} + 6x^{-1/2}.\)

This one is a lot harder. It is obvious that 3 is a common factor in each term, but it may be harder to see that \(\displaystyle x^{-1/2}\) is also a common factor.

\(\displaystyle x^{3/2} = x^{4/2} * x^{-1/2} = x^2 * x^{-1/2} \text { and } x^{1/2} = x^{2/2} * x^{-1/2} = x * x^{-1/2}.\)

\(\displaystyle \therefore 3x^{3/2} - 9x^{1/2} + 6x^{-1/2} = 3(x^{3/2} - 3x^{1/2} + 2x^{-1/2})=\)

\(\displaystyle 3x^{-1/2}(x^2 - 3x + 2) = \dfrac{3(x - 2)(x - 1)}{\sqrt{x}} = \dfrac{3(x - 2)(x - 1)\sqrt{x}}{x}.\)
 
Top