Two questions - factoring and exponents

In summary, these are not homework questions. They were on a test I had today. The first was about how to factor a 2x^3-3x^2-16x-5 and I just used my graphing utility to find the answer. I'm fairly certain that's right. The second question was about exponents and I think I got this one wrong. The final question was about a rational expression and I didn't get it right. I think I need to divide it out and then the oblique asymptote is the line y = [the answer excluding the remainder].
  • #1
superdave
150
3
These aren't homework questions. They were on a test I had today.

The first was how do I factor 2x^3-3x^2-16x-5. I'm fairly certain that's right. It was actually part of a larger problem, involving finding a slant asymptote. I just used my graphing utility to find the answer, but I'd like to know how to actually factor that. I'm pretty sure you get (x+1) and a quadratic equation, just not sure what that equation is.

Second question is about exponents. I think I got this one wrong.

It was 1.7^(-3/5). Now, I got .787 I think. But what I was wondering, shouldn't the answer be equal to 1.7^-3 - 1.7^5? When I tested it, it wasn't. Isn't that one of the properties of exponents? x^(a/b) = x^a-x^b?
 
Physics news on Phys.org
  • #2
superdave said:
shouldn't the answer be equal to 1.7^-3 - 1.7^5?

No, what it should be is [tex] \frac{x^a}{x^b} = x^{a-b} [/tex].

Also, I hate to break it to you, but I don't think that x+1 is a factor of that cubic (unless my mental maths is wrong - which is quite likely). To factor that, you might be able to find a root, by substituting numbers in and seeing if you get 0. Then, use polynomial division (assuming you can do that), to reduce the degree by 1, and then use the quadratic formula to get the other two roots.

You could always look at the co-efficients of the terms, e.g. the product of the three roots will equal 5/2, that might help.
 
Last edited by a moderator:
  • #3
err, I meant x-1.
 
  • #4
superdave said:
err, I meant x-1.

Still doesn't work.

-Dan
 
  • #5
Are you sure that that is what you need to factor? I ask this because this doesn't have nice roots. The roots are approximately -1.947985, -.3389005, and 3.7868854. So the factored form would look something like this:

f(x) = (x+1.948)(x+.3389)(x-3.787).
 
  • #6
No. I could be remembering wrong. I didn't actually have to factor it. The question was about finding a slant asymptote. I assumed there was factoring. But it was too hard, so I just used my TI 84 to graph it, then found the asymptote through trial and error. (It was a multiple choice question. I just put in each option and looked to see if it worked with the other function.)

When we get our tests back Monday, I'll put the problem up. Cause I would like to know if there was an easy way. The final exam is not multiple choice, so it won't work for that.
 
  • #7
Do you realize that there is no slant asymptote on that graph?

Are you sure it wasn't dealing with a different graph or something?
 
  • #8
Maybe that was the numerator of a rational expression. In this case, you would divide it out and then the oblique asymptote is the line y = [the answer excluding the remainder].
 

1. What is factoring and why is it important?

Factoring is the process of breaking down a mathematical expression into smaller, simpler parts. It is important because it allows us to simplify and solve more complex equations, as well as identify patterns and relationships between numbers.

2. What are the different methods of factoring?

There are several methods of factoring, including common factor, difference of squares, grouping, and quadratic formula. The method used depends on the type of expression and the specific factors involved.

3. Can factoring be used to solve equations with exponents?

Yes, factoring can be used to solve equations with exponents. In these cases, the goal is to factor out the common base and use the properties of exponents to simplify the equation.

4. What is the difference between factoring and expanding?

Factoring involves breaking down an expression into smaller parts, while expanding involves combining multiple expressions into a larger one. They are essentially inverse operations of each other.

5. How does factoring relate to real-life situations?

Factoring can be used in real-life situations to solve problems involving numbers, patterns, and relationships. It can also help in simplifying and analyzing complex data, such as in financial analysis or scientific experiments.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
6
Views
1K
  • Precalculus Mathematics Homework Help
Replies
2
Views
803
  • Precalculus Mathematics Homework Help
Replies
13
Views
561
  • Precalculus Mathematics Homework Help
Replies
6
Views
546
  • Precalculus Mathematics Homework Help
Replies
13
Views
2K
  • Precalculus Mathematics Homework Help
Replies
13
Views
2K
  • Precalculus Mathematics Homework Help
Replies
1
Views
1K
  • Precalculus Mathematics Homework Help
Replies
10
Views
567
  • Precalculus Mathematics Homework Help
Replies
10
Views
508
  • Precalculus Mathematics Homework Help
Replies
6
Views
1K
Back
Top