Question

Factorizar:
A(x) = x⁴– 37x² + 36​

Answer 1

Respuesta:

$=\left(x+1\right)\left(x-1\right)\left(x+6\right)\left(x-6\right)$

Explicación paso a paso:

$x^4-37x^2+36$

$\mathrm{Sea\:}u\mathrm{=}x^2$

$=u^2-37u+36$

$\mathrm{Factorizar}\:u^2-37u+36:\quad \left(u-1\right)\left(u-36\right)$

$=\left(u-1\right)\left(u-36\right)$

$\mathrm{Sustituir\:en\:la\:ecuacion}\:u=x^2$

$=\left(x^2-1\right)\left(x^2-36\right)$

$\mathrm{Factorizar}\:x^2-1:\quad \left(x+1\right)\left(x-1\right)$

$=\left(x+1\right)\left(x-1\right)\left(x^2-36\right)$

$\mathrm{Factorizar}\:x^2-36:\quad \left(x+6\right)\left(x-6\right)$

$=\left(x+1\right)\left(x-1\right)\left(x+6\right)\left(x-6\right)$