Question

phân tích các đa thức sau thành nhân tử :

a)x⁸+x+1

b)x⁸+3x⁴+4

Answer 1

a) x⁸ + x + 1 = (x^2+x+1)*(x^6-x^5+x^3-x^2+1)

b) x^8 + 3x^4 + 4 = (x^4-x^2+2)*(x^4+x^2+2)

Answer 2

\(x^8+x+1\)

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

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

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

Answer 3

\(x^8+3x^4+4\)

\(=x^8+4x^4+4-x^4\)

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

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