So from the final two terms it looks like the

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Unformatted text preview: thetic division and this time we’ll just put up the results and leave it to you to check all the actual numbers. -2 2 0 -3 - 5 -4 8 -10 2 -4 So, in this case we have, 5 -15 2 x 3 - 3x - 5 = ( x + 2 ) ( 2 x 2 - 4 x + 5 ) - 15 [Return to Problems] (b) Divide 4 x 4 - 10 x 2 + 1 by x - 6 In this case we’ve got r=6. Here is the work. 6 4 0 -10 0 1 0 24 144 804 4824 4 24 134 804 4825 In this case we then have. 4 x 4 - 10 x 2 + 1 = ( x - 6 ) ( 4 x3 + 24 x 2 + 134 x + 804 ) + 4825 [Return to Problems] So, just why are we doing this? That’s a natural question at this point. One answer is that, down the road in a later section, we are going to want to get our hands on the Q(x). Just why we might want to do that will have to wait for an explanation until we get to that point. There is also another reason for this that we are going to make heavy usage of later on. Let’s first start out with the division algorithm. P ( x) = ( x - r )Q ( x) + R Now, let’s evaluate the polynomial P(x) at r. If we had an actual polynomial here we could evaluate P(x) directly of course, but let’s use t...
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