Expert: Abe Mantell - 1/9/2005

Question
I'm having trouble with Polynomial Long Division, especially with this problem. How do you do it?

( x^3 + 7x - 8 ) / ( x - 3 )

Answer
Hello Olsi (interesting name...what is it?),

Long division of polynomials is similar to ordinary
long division.  Here are some web-sites that have
good graphics:
http://www.sosmath.com/algebra/factor/fac01/fac01.html
http://www.purplemath.com/modules/polydiv2.htm
http://www.mathwords.com/p/polynomial_long_division.htm
http://www.math.utah.edu/online/1010/euclid/
http://tutorial.math.lamar.edu/AllBrowsers/1314/DividingPolynomials.asp

But I will try and walk you through your problem...

What do we need to multiply x (as in x-3) by to match
x^3?  x^2 of course!
Now multiply x-3 by x^2 and subtract the result from
x^3 + 7x - 8: x^3 + 7x - 8 - (x^3-3x^2) = 3x^2+7x-8
Now, what do we need to multiply x by to match 3x^2? 3x
Now multiply x-3 by 3x and subtract the result from
3x^2+7x-8: 3x^2+7x-8 - (3x^2-9x) = 16x-8
Now nultiply x-3 by 16 and subtract from 16x-8,
giving: 16x-8 -(16x-48) = 40

So, the result is: x^2+3x+16 with remainder 40

OK?

TTYL, Abe