Algebra Question(Part of a Larger Problem)

  • Thread starter Thread starter undrcvrbro
  • Start date Start date
  • Tags Tags
    Algebra
Click For Summary
The discussion revolves around simplifying the algebraic expression f(x) = (2x)(x-5)^(3) + 3x^2(x-5)^(2). The user initially struggles with the simplification and seeks guidance, noting that the book's answer is 5x(x-5)^(2)(x-2). A key suggestion is to factor out the common term x*(x-5)^(2), which leads to a clearer path for simplification. After some back-and-forth, the user realizes their mistake and successfully simplifies the expression. The interaction highlights the importance of identifying common factors in algebraic expressions.
undrcvrbro
Messages
131
Reaction score
0

Homework Statement


f(x) = (2x)(x-5)^(3) + 3x^2(x-5)^(2)

Need to simplify.


Homework Equations





The Attempt at a Solution


I tried simplifying completely but my answer wasn't even close. The Back of the book has:
5x(x-5)^(2)(x-2)

I know its easy, but I'm drawing a blank...can anyone start me off on the right path to find how they got that answer?
 
Physics news on Phys.org
The first thing to notice is that both terms in your expression have a common factor of x*(x-5)^2. Factor that out. Now what's left in each term?
 
Well, wouldn't it then be 2(x-5) + (3x+1)?
 
I get just 2(x-5)+3x. Where did the 1 come from?
 
Oh! I got it!

Oh wow. I can't believe I had made a mistake like that. Thank you so much. I just figured it out.

Thanks Dick.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Question on Two Differentiation Techniques
  • · Replies 25 ·
Replies
25
Views
2K
How Do You Simplify and Analyze Taylor Polynomials for Higher Degree Functions?
  • · Replies 5 ·
Replies
5
Views
2K
Finding the Fourier Series of a step function
  • · Replies 5 ·
Replies
5
Views
3K
Odd/even function and critical points
  • · Replies 4 ·
Replies
4
Views
3K
Minimize integral using orthogonal basis
  • · Replies 2 ·
Replies
2
Views
1K
Cauchy-Riemann Condition Verification for f(z) = z^3-5iz+√7
  • · Replies 11 ·
Replies
11
Views
3K
Limits...what am I doing wrong ? (Without hopital)
  • · Replies 2 ·
Replies
2
Views
1K
Constructing a splitting field for polynomial over F_5
  • · Replies 5 ·
Replies
5
Views
2K
Derivative of Secant: Find dy/dx
  • · Replies 2 ·
Replies
2
Views
1K
Solving Limits: Finding a, b, c, and d for ∞-∞ Form
  • · Replies 2 ·
Replies
2
Views
1K