Standard form of 40+2+.3+.08
2 answers:
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If you're familiar with synthetic division, but not the extended form (which allows you easily compute the quotient/remainder when dividing a polynomial by another polynomial of degree greater than 1), then you can perform two steps of SD.
Instead of dividing by
, first divide by 
, then by 
(since 
). So we have
0 | 1 4 2 1 4
... | 0 0 0 0
= = = = = = = = = = = =
... | 1 4 2 1 4
which translates to
Ignoring the remainder term for now, the next round of SD yields
-3 | 1 4 2 1
... | -3 -3 3
= = = = = = = = = =
... | 1 1 -1 4
which translates to
Now, putting everything together, we have
which is to say the remainder upon dividing
by is 
.
Instead of dividing by
0 | 1 4 2 1 4
... | 0 0 0 0
= = = = = = = = = = = =
... | 1 4 2 1 4
which translates to
Ignoring the remainder term for now, the next round of SD yields
-3 | 1 4 2 1
... | -3 -3 3
= = = = = = = = = =
... | 1 1 -1 4
which translates to
Now, putting everything together, we have
which is to say the remainder upon dividing