Question

Phân tích đa thức sau thành nhân tử

a) x⁷+ x² + 1

b) x^{5 +} x⁴ + 1

c) x⁸ + x + 1

d) x⁷ + x⁵+1

Answer 1

 

a) x⁷+ x² + 1

=x⁷-x+x²+x+1

=x.(x⁶-1)+(x²+x+1)

=x.(x³-1)(x³+1)+(x²+x+1)

=x.(x-1)(x²+x+1)(x³+1)+(x²+x+1)

=(x²+x+1)[x.(x-1)(x³+1)+1]

=(x²+x+1)(x⁵+x²-x⁴-x+1)

 

b) x⁵ + x⁴ + 1

=x⁵+x⁴+x³+x²+x+1-x³-x²-x

=x³.(x²+x+1)+(x²+x+1)-x.(x²+x+1)

=(x²+x+1)(x³+1-x)

 

   

Answer 2

\(x^8+x+1\)

\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)

\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)

Answer 3

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

\(=x^5+x^4+x^3-x^3-x^2-x+x^2+x+1\)

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

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