Question

Phân tích đa thức thành nhân tử: x^8 + x + 1

Answer 1

đề sai ko?

Answer 2

ta có: x^8 +x+1= (x^8 -x^5) +(x^5 -x^2)+x^2 +x+1=x^5(x^3-1) +x^2(x^3-1) +x^2+x+1=x^5(x-1)(x^2+x+1) +x^2(x-1)(x^2+x+1)+x^2 +x+1=(x^2 +x+1)(x^6-x^5+x^3 -x^2 +1)

Answer 3

Ta có : x⁸ + x + 1

= x⁸ - x⁵ + x⁵ - x² + x² + x + 1

= (x⁸ - x⁵)  + (x⁵ - x²) + x² + x + 1

= x⁵(x³ - 1) + x²(x³ - 1) + x² + x + 1

= x⁵(x - 1)(x² + x + 1) + x²(x - 1)(x² + x + 1) +  x² + x + 1

= x⁶ - x⁵ (x² + x + 1) + x³ - x² (x² + x + 1) + (x² + x + 1)

= ( x² + x + 1)(x⁶ - x⁵ + x³ - x² + 1) 

Answer 4

\(x^8+x+1\)

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

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

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