Question

phân tích đa thức thành nhân tử:

a) x^5+x^4+1

b) x^3-7x+6

Answer 1

a) \(x^5+x^4+1\)

=\(x^5+x^4+x^2-x^2+1\)

=\(x^2\left(x^3-1\right)+\left(x^4+x^2+1\right)\)

=x²(x-1)(x²+x+1)+(x⁴+2x²+1-x²)

=\(\left(x^3-1\right)\left(x^2+x+1\right)+\left[\left(x^2+1\right)^2-x^2\right]\)

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

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

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

b)

Answer 2

b) x^3-7x-6

=x^3-x-6x-6

=x(x^2-1)-6(x+1)

=x(x-1)(x+1)-6(x+1)

=(x^2-x-6)(x+1)

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