Solving a Factoring Problem in Calculus without a Calculator

  • Thread starter zombeast
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In summary, the student is practicing graphing without a calculator for an upcoming test in calculus. They are asking for help with factoring a polynomial and have received tips from others. They eventually figure out the correct factored form.
  • #1
zombeast
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I'm in calculus, but we're having this test on some curve sketing soon and I'm doing some practice problems that the teacher gave us. We're not allowed to use a calculator in this calculus class (except for very rare instances) so we have to know how to sketch graphs with no problem!

I'm wondering I have factored this correctly. If not, I'm wondering if someone can point me in the right direction.

Orginal Equation:
[tex]
x^3 - 3x^2-6x+8
[/tex]

My Factors
[tex]
(x+2)(x^2-2x+4) - 3x(x+2)
[/tex]

Turns into ...

[tex]
(1-3x)(x+2)(x^2 -2x + 4)
[/tex]

If anyone could help me out I would appreciate it.

Thanks!
 
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  • #2
You can always multiply them back out to see if it gets you where you started.
 
  • #3
Your original polynomial has degree 3 yet you have 4 factors involving x!

Hint: [tex](x+2)(x^2-2x+4) - 3x(x+2) [/tex] is correct but
ab- ca= a(b- c) NOT ab(1-c).
 
  • #4
Ok, thanks for the help thus far. I was able to remember (through the help of another math friend) that if all the coefficients of the polynomial add up to zero, it is divisble by x-1 and x-1 is one of the factors. Therefore I had to take x-1 and divide it into [tex]x^3 - 3x^2 -6x+8[/tex] and I was given [tex]x^2-2x-8[/tex]. From that I could get the other two factors [tex](x-4)(x+2)[/tex]

Thanks for looking at it though.
 
  • #5
Your factored expression is a 4th degree polynomial while your original expression is a 3rd degree polynomial.

As HallsofIvy said, [tex](x+2)(x^2-2x+4) - 3x(x+2) [/tex] is correct, and the factored form should be

(x+2)(2nd degree poly).
 

1. How do I solve a factoring problem in Calculus without a calculator?

To solve a factoring problem in Calculus without a calculator, you can use the following steps:

  • Step 1: Identify the common factor between the terms.
  • Step 2: Use the distributive property to remove the common factor.
  • Step 3: Factor the remaining terms using techniques such as grouping or the difference of squares.
  • Step 4: Check your factored expression by expanding it and making sure it is equivalent to the original expression.

2. Can I use a calculator to solve a factoring problem in Calculus?

Technically, you can use a calculator to solve a factoring problem in Calculus. However, it is important to understand the concept of factoring and be able to solve problems without a calculator as it is a fundamental skill in Calculus and other higher level math courses.

3. How can I check if my factored expression is correct?

You can check if your factored expression is correct by expanding it and making sure it is equivalent to the original expression. You can also use the distributive property to simplify your factored expression and see if it matches the original expression.

4. Are there any tips for factoring in Calculus without a calculator?

Yes, here are a few tips for factoring in Calculus without a calculator:

  • Try to identify common factors between the terms.
  • Use techniques such as grouping or the difference of squares.
  • Practice factoring by doing more problems and familiarizing yourself with common patterns.

5. Why is it important to be able to solve factoring problems in Calculus without a calculator?

Being able to solve factoring problems in Calculus without a calculator is important because it helps you develop a deeper understanding of mathematical concepts and builds your problem-solving skills. It also prepares you for higher level math courses where calculators may not be allowed. Additionally, being able to factoring without a calculator can save time and help you check your work for accuracy.

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