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**Unformatted text preview: **ormed
at the beginning of the section and try to streamline it. First oﬀ, let’s change all of the subtractions
into additions by distributing through the −1s.
x2 + 6 x + 7
x−2 x3 + 4x2 − 5x −14
−x3 + 2x2
6x2 − 5x
−6x2 + 12x
7x −14
−7x+14
0
Next, observe that the terms −x3 , −6x2 , and −7x are the exact opposite of the terms above them.
The algorithm we use ensures this is always the case, so we can omit them without losing any
3
4 Yes, Virginia, there are algebra courses more abstract than this one.
Jeﬀ hates this expression and Carl included it just to annoy him. 3.2 The Factor Theorem and The Remainder Theorem 199 information. Also note that the terms we ‘bring down’ (namely the −5x and −14) aren’t really
necessary to recopy, and so we omit them, too.
x2 + 6 x + 7
x−2 x3 +4x2 − 5x −14
2x2
6x2
12x
7x
14
0
Now, let’s move things up a bit and, for reasons which will become clear in a moment, copy the x3
into the last row.
x2 + 6 x + 7
x−2 x3 +4x2 − 5x −14
2x2 12x 14
x3...

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