Question

Phân tích đa thức thành nhân tử:

a) \(x^4+x^3+2x^2+x+1\)

b) \(\left(x^3+3x+1\right)\left(x^3+3x+2\right)-6\)

Answer 1

Answer 2

b) $\left(x^3+3x+1\right)(x^3+3x+2)-6$

đặt x³+3x+1=a ta có

a(a+1)-6

=a²+a-6

=a²+3a-2a-6

=a(a+3)-2(a+3)

=(a-2)(a+3)

thay a=x³+3x+1 vào ta đc

( x³+3x+1-2)(x³+3x+1+3)

= (x³+3x-1)(x³+3x+4)

Answer 3

a) x⁴+x³+2x²+x+1

= (x⁴+2x²+1)+(x³+1)

=(x²+1)²+x(x²+1)

= (x²+1)(x²+x+1)