Help with Extension Maths (1 Viewer)

[LC14199]

Hey guys, I'm having some problems with the following Polynomial equations.

The question states the following:
"The remainder is 5 when P(x)= ax^3-4bx^2+x-4 is divided by x-3 and the remainder is 2 when P(x) is divided by x+1. Find the values of a and b."

I am aware that these will create two equations that need to be solved simultaneously, however I am having issues solving it. I do not know why, but larger simultaneous equations become quite irritating for me... If you could show me how to solve this one step by step, I could apply the same working to all the questions in this exercise and hopefully begin to understand the process.

Cheers,
LC14199

 

[element101anushrium]

My school isn't up to polynomials because we have assessment week currently but from what I can remember from last year, I know a thing or two about dividing the polynomials. Except, the question looks daunting with the "a" and "b".

I tried it without the a and b where I divided P(x)= x^3-4x^2+x-4 by x-3....and.....got (x-2)(x^2-x-2)-10....which I don't know if that's the correct answer. For the second equation.....I would do the same as well....

Then....simultaneously solve the equations....you will maybe cancel the x's.

Then just sub back the x value and then....I don't know...

But I'll try to work out the question myself and reply with working out and stuff if I can solve it.

 

[element101anushrium]

If you end up solving it, can you please tell me how?

Thanks.

 

[VBN2470]

No need for polynomial long division, the remainder theorem already accounts for that, so it makes the calculations easier to compute.

 

[element101anushrium]

Ahhh






I don't know what the polynomial remainder theorem but probably will do it next term.

Thanks.

 

[LC14199]

Indeed, my question resides in solving these two simultaneously. I am unsure what to do. I will seek some help today, and post back with results if I get any.

 

[ertceps]

Here you go! Decimal values for b and a are horrible...
Sorry if my working out is unclear
http://i.imgur.com/Zp56v2q.jpg

 

[LC14199]

Quoting my maths teacher "There is no such thing as decimals if you wish to be exact". Lmao such a true statement. Your working is similar to mine, except I did mine in fraction form. But there we go.

PS: Sorry I necro'd a VERY old thread xD

 

[InteGrand]

Quoting my maths teacher "There is no such thing as decimals if you wish to be exact". Lmao such a true statement. Your working is similar to mine, except I did mine in fraction form. But there we go.

Recurring decimals are still exact.

 

[LC14199]

However B was rounded, which therefore makes the answer inexact. Hence my response.

Anyways it's done, solved, problem is no longer existant haha.

Thanks for the help guys

 

[Speed6]

/closethread