Question

分解因式：x的五次方-x的四次方-x+1 ②p的四次方-3乘以p的三次方+7乘以p的二次方+6p-18

Answer 1

x的五次方-x的四次方-x+1

=x^4(x-1)-(x-1)

=(x-1)(x^4-1)

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

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

p^4-3p^3+7p^2+6p-18

【3p^2-6=0,p=√2

4+14-18=0】

p^4+7p^2-18-3p（p^2-2)

=(p^2-2)(p^2+9)-3p（p^2-2)

=（p^2-2)(p^2-3p+9)

=(p-√2）（p+√2）（p^2-3p+9)