Lets again start with the integers and see what we

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Unformatted text preview: ar synthetic division if you need to, but it’s a good idea to be able to do these tables as it can help with the process. Okay, back to the problem. We now know that x = 1 is a zero and so we can write the polynomial as, P ( x ) = x 4 - 7 x3 + 17 x 2 - 17 x + 6 = ( x - 1) ( x 3 - 6 x 2 + 11x - 6 ) Now we need to repeat this process with the polynomial Q ( x ) = x 3 - 6 x 2 + 11x - 6 . So, the first thing to do is to write down all possible rational roots of this polynomial and in this case we’re lucky enough to have the first and last numbers in this polynomial be the same as the original polynomial, that usually won’t happen so don’t always expect it. Here is the list of all possible rational zeroes of this polynomial. ±1, ± 2, ± 3, ± 6 Now, before doing a new synthetic division table let’s recall that we are looking for zeroes to P ( x ) and from our first division table we determined that x = -1 is NOT a zero of P ( x ) and so there is no reason to bother with that number again. This is something that we should always do at this step. Take a look at the list of new possible rational zeros and ask a...
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