How do you use synthetic division to divide (x3−8x2−25x+203) by x−5?

1 Answer
George C.
May 23, 2015

Synthetic division is somewhat like long division.

Starting with (x3−8x2−25x+203), first look for a multiplier for (x−5) that will cause give a match for the highest order term.

Choose x2 as the first multiplier.

x2(x−5)=x3−5x2

Subtract this from our original polynomial to get the remainder:

(x3−8x2−25x+203)−(x3−5x2)

=(−3x2−25x+203)

Now choose a multiplier (−3x) for (x−5) to match the leading term −3x2 of the remainder...

(−3x)(x−5)=(−3x2+15x)

Subtract this from our remainder to get a new remainder:

(−3x2−25x+203)−(−3x2+15x)=(−40x+203)

Now choose a multiplier (−40) for (x−5) to match the leading term −40x of our remainder...

(−40)(x−5)=(−40x+200)

Subtract this from our remainder to get a new remainder:

(−40x+203)−(−40x+200)=3

Adding our multipliers together, we find:

x3−8x2−25x+203=(x−5)(x2−3x−40)+3

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