HighSchool Calculus Polynomial Division Help

In summary, the conversation is about a question involving dividing polynomials and determining the value of a variable p. The method involves using polynomial division and setting the remainder equal to a given value. There is some confusion about the steps involved, but the participants eventually figure it out with the help of each other. They also discuss using a web cam to better explain the process.
  • #1
Hollysmoke
185
0
I was just doing my homework when I stumbled on this question. I don't understand it and I was wondering if someone could help me through it (don't just do it though, because I want to learn HOW to do it :smile: )

When 8x^3+4x^2-px+6, p E R, is divided by 2x-1, the remainer is 3. Determine the value of p.

Thank you (And sorry about the question, I don't know how to use the LaTex stuff yet)
 
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  • #2
Have you ever done a 'long division' on polynomials, perhaps easier ones?
 
  • #3
Yeah, then I hit this question and I got lost. The unit is Chapter 1.4-Dividing Polynomials
 
  • #4
I'm confused, I didn't use any calculus at all to solve it. This is how I did it...I used polynomial division (I'm assuming you can do that reasonably well), and then towards the end, I got (-p+4)x = -6x, and then solved that. This would be so much easier if I had a web cam to show my working. It would also make much more sense to you, since I wouldn't be surprised if you had no idea what I was talking about.
 
  • #5
Just do polynomial division as usual until you get the remainer (which should contain the variable p). Equal that to 3 and you'll get the answer.
 
  • #6
Hollysmoke said:
Yeah, then I hit this question and I got lost. The unit is Chapter 1.4-Dividing Polynomials
Although it's a bit more work, the method is the same for larger polynomials and you can just consider p as an unknown parameter for now. See if you can get started on the division, unfortunately it's rather hard to display such a long division on the forum.
 
  • #7
I wrote it out but I think I'm doing something wrong. While dividing, I get to the step 8x^2-px - 8x^2-4x
 
  • #8
Hollysmoke said:
I wrote it out but I think I'm doing something wrong. While dividing, I get to the step 8x^2-px - 8x^2-4x
Assuming that you mean [itex]8x^2-px - (8x^2-4x)[/itex], that's fine since that equals [itex]x(p-4)[/itex] which is exactly what finchie_88 found as well so I think you're on track!
 
  • #9
OHH I SEE NOW. I get -px+4x, so I factor the x out?
 
  • #10
I got it! THank you so much XD
 
  • #11
Great :smile:
 

Related to HighSchool Calculus Polynomial Division Help

What is polynomial division in high school calculus?

Polynomial division in high school calculus is a method used to divide one polynomial function by another. It involves dividing the terms of the dividend by the terms of the divisor, similar to long division with numbers.

Why is polynomial division important in high school calculus?

Polynomial division is important in high school calculus because it helps us solve complex algebraic equations and find the roots of polynomial functions. It is also necessary for finding the derivative of polynomial functions.

What are the steps for polynomial division in high school calculus?

The steps for polynomial division in high school calculus are: 1) Arrange the terms of the dividend and divisor in descending order of their exponents. 2) Divide the first term of the dividend by the first term of the divisor to get the first term of the quotient. 3) Multiply the first term of the quotient by the entire divisor and subtract it from the dividend. 4) Bring down the next term of the dividend and repeat the process until you have no more terms to bring down. 5) The resulting quotient is the answer.

What are some common mistakes students make when doing polynomial division in high school calculus?

Some common mistakes students make when doing polynomial division in high school calculus are: 1) Not arranging the terms of the dividend and divisor in descending order of their exponents. 2) Forgetting to bring down the next term of the dividend. 3) Making a mistake in the division or subtraction process. 4) Not simplifying the resulting quotient. 5) Not checking their final answer for accuracy.

How can I improve my understanding and skills in polynomial division for high school calculus?

You can improve your understanding and skills in polynomial division for high school calculus by practicing regularly, asking your teacher for help when needed, and seeking additional resources such as textbooks, online tutorials, and practice problems. It is also important to review the basic concepts of polynomial functions and algebra before attempting polynomial division.

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