Question

分解因式 a三次方－5a平方＋5a－4,(1＋x＋x平方＋x三次方）平方－x三次方

Answer 1

a^3-5a^2+5a-4

=a^3-5a^3+4a+a-4

=a(a^2-5a+4)+a-4

=a(a-1)(a-4)+(a-4)

=(a-4)(a^2-a+1)

(1+x+x^2+x^3)^2-x^3

=(1+x+x^2+x^3)^2-1+1-x^3

=(x+x^2+x^3)(2+x+x^2+x^3)+(1-x)(1+x+x^2)

=(1+x+x^2)[x*(2+x+x^2+x^3)+1-x]

=(1+x+x^2)(1+x+x^2+x^3+x^4)