How do you use synthetic division to divide $(x^3 -8 x^2 - 25x + 203)$ by $x-5$ ?

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Answer 1 · 2015-05-23T00:36:02

Synthetic division is somewhat like long division.

Starting with $(x^3-8x^2-25x+203)$ , first look for a multiplier for $(x-5)$ that will cause give a match for the highest order term.

Choose $x^2$ as the first multiplier.

$x^2(x-5) = x^3-5x^2$

Subtract this from our original polynomial to get the remainder:

$(x^3-8x^2-25x+203) - (x^3 - 5x^2)$

$= (-3x^2-25x+203)$

Now choose a multiplier $(-3x)$ for $(x-5)$ to match the leading term $-3x^2$ of the remainder...

$(-3x)(x-5) = (-3x^2+15x)$

Subtract this from our remainder to get a new remainder:

$(-3x^2-25x+203) - (-3x^2+15x) = (-40x+203)$

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:

$x^3-8x^2-25x+203 = (x-5)(x^2-3x-40) + 3$

How do you use synthetic division to divide (x^3 -8 x^2 - 25x + 203)(x^3 -8 x^2 - 25x + 203) by x-5x-5?