Alg_Complete

# This will always happen with every polynomial and we

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ( x ) = x3 + 2 x 2 - 5 x - 6 the Fact 1 tells us that we can write P ( x ) as, P ( x ) = ( x - 2) Q ( x ) and Q ( x ) will be a quadratic polynomial. Then we can find the zeroes of Q ( x ) by any of the methods that we’ve looked at to this point and by Fact 2 we know that the two zeroes we get from Q ( x ) will also by zeroes of P ( x ) . At this point we’ll have 3 zeroes and so we will be done. So, let’s find Q ( x ) . To do this all we need to do is a quick synthetic division as follows. © 2007 Paul Dawkins 253 http://tutorial.math.lamar.edu/terms.aspx College Algebra 21 1 2 -5 -6 286 4 3 0 Before writing down Q ( x ) recall that the final number in the third row is the remainder and that we know that P ( 2 ) must be equal to this number. So, in this case we have that P ( 2 ) = 0 . If you think about it, we should already know this to be true. We were given in the problem statement the fact that x = 2 is a zero of P ( x ) and that means that we must have P ( 2 ) = 0 . So, why go on about this? This is a great check of our synthetic division. Sin...
View Full Document

## This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

Ask a homework question - tutors are online