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**Unformatted text preview: **6x2 7x 0
Note that by arranging things in this manner, each term in the last row is obtained by adding the
two terms above it. Notice also that the quotient polynomial can be obtained by dividing each of
the ﬁrst three terms in the last row by x and adding the results. If you take the time to work back
through the original division problem, you will ﬁnd that this is exactly the way we determined the
quotient polynomial. This means that we no longer need to write the quotient polynomial down,
nor the x in the divisor, to determine our answer.
−2 x3 +4x2 − 5x −14
2x2 12x 14
x3 6x2 7x 0
We’ve streamlined things quite a bit so far, but we can still do more. Let’s take a moment to
remind ourselves where the 2x2 , 12x, and 14 came from in the second row. Each of these terms
was obtained by multiplying the terms in the quotient, x2 , 6x and 7, respectively, by the −2 in
x − 2, then by −1 when we changed the subtraction to addition. Multiplying by −2 then by −1
is the same as multiplying by 2, and so we...

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