HighSchool Calculus Polynomial Division Help

[Hollysmoke]

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 )

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)

 

[TD]

Have you ever done a 'long division' on polynomials, perhaps easier ones?

 

[Hollysmoke]

Yeah, then I hit this question and I got lost. The unit is Chapter 1.4-Dividing Polynomials

 

[finchie_88]

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.

 

[assyrian_77]

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.

 

[TD]

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.

 

[Hollysmoke]

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

 

[TD]

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 $8x^2-px - (8x^2-4x)$, that's fine since that equals $x(p-4)$ which is exactly what finchie_88 found as well so I think you're on track!

 

[Hollysmoke]

OHH I SEE NOW. I get -px+4x, so I factor the x out?

 

[Hollysmoke]

I got it! THank you so much XD

 

[TD]

Great