Expert: Richard J. Raridon - 9/8/2009

Question
Hello! I was learning about synthetic division of polynomials a while ago, but one thing always puzzled me: why we did the 'test zero'.

see this website: http://mathcentral.uregina.ca/QQ/database/QQ.09.06/h/edward1.html

Alright. So on the left side of the reversed division symbol, it is a 2. The original question was x-2, so why would we not put -2 in it? I know that it states "So set x-2=0, then x=2", but i do not understand thoroughly what it means. Could you please explain setting zeros, and why the number is reversed ? Thanks!

Answer
First of all, if x-2=0, then obviously, x=2.  They never taught synthetic division when I took algebra 60 years ago.  I just did it like long division.  For example, if you're going to divide x-2 into 3x^3 +2x^2 +4, the first number in the quotient is 3x^2.  Multiply that by x-2 and you get 3x^3-6x^2.  Subtract that from the dividend and you have 8x^2+4.  So the second number in the quotient is 8x.  Multiply that by x-2 and you get 8x^2-16x.  Subtract that from 8x^2+4 and you have 16x+4.  So the last number in the quotient is 16.  Multiply that by x-2 and you get 16x-32. Again, subtract that from 16x+4 and you have 36.  Therefore, your answer is 3x^2+8x+16 with a remainder of 36.  Write that down like a long division problem and maybe it will make more sense.