This will always happen with every polynomial and we

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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...
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