Question

Operaciones con polinimios : Division

(X⁴₋7x³ ₊ 18x²₋ 20x ₊ 8) ÷ (X²₋ 4x ₊ 4)

Answer 1

$\frac{x^4-7x^3+18x^2-20x+8}{x^2-4x+4}$

$\mathrm{Factorizar}\:x^4+18x^2-7x^3-20x+8:$
$=\left(x-1\right)\left(x-2\right)\left(x-2\right)\left(x-2\right)$
$=\left(x-2\right)^3\left(x-1\right)$
$=\frac{\left(x-2\right)^3\left(x-1\right)}{x^2-4x+4}$
$\mathrm{Factorizar}\:x^2-4x+4:$
$=\left(x-2\right)\left(x-2\right)$
$=\left(x-2\right)^2$
$=\frac{\left(x-2\right)^3\left(x-1\right)}{\left(x-2\right)^2}$
$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad \frac{x^a}{x^b}\:=\:x^{a-b}$
$\frac{\left(x-2\right)^3}{\left(x-2\right)^2}=\left(x-2\right)^{3-2}=x-2$
=(x-2)(x-1)