Question

Faça a fatoração completa

 

a) m³ - m

b) $<var>x^{5}-9x^{3} </var>$

c) $<var>x^{4}-y^{4}</var>$

d) $<var>5x^{4}-5</var>$

Answer 1

a) $m^3-m = m(m^2-1) = m(m-1)(m+1)$

b) $x^5-9x^3 = x^3(x^2-9) = x^3(x-3)(x+3)$

c) $x^4-y^4 = (x^2-y^2)(x^2+y^2) = (x-y)(x+y)(x^2+y^2)$
$= (x-y)(x+y)((x+y)(x+y)-2xy)$

d) $5x^4-5 = 5(x^4-1) = 5(x^2-1)(x^2+1) = 5(x-1)(x+1)(x^2+1)$
$= 5(x-1)(x+1)((x+1)(x+1)-2x)$