How do you use polynomial synthetic division to divide $(x^6-6x^4+12x^2-8)div(x+sqrt2)$ and write the polynomial in the form $p(x)=d(x)q(x)+r(x)$ ?

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Answer 1 · 2017-07-10T18:29:11

$q(x) = x^5 - x^4 sqrt 2 -4 x^3 + 4 x^2 sqrt 2 + 20 x - 20 sqrt 2$
$r(x) = 32$

Briot Ruffini

$((),(-sqrt 2)) ((1),(1)) ((0),(-sqrt 2)) ((-6),(-4)) ((0),(4 sqrt 2)) ((12),(20)) ((0),(- 20 sqrt 2)) ((-8),(32))$

$p(x)=d(x)q(x)+r(x)$

$d(x) = x + sqrt 2$

$q(x) = x^5 - x^4 sqrt 2 -4 x^3 + 4 x^2 sqrt 2 + 20 x - 20 sqrt 2$

$r(x) = 32$

How do you use polynomial synthetic division to divide (x^6-6x^4+12x^2-8)div(x+sqrt2)(x^6-6x^4+12x^2-8)div(x+sqrt2) and write the polynomial in the form p(x)=d(x)q(x)+r(x)p(x)=d(x)q(x)+r(x)?