Question

Phân tích các đa thức sau thành nhân tử

X mũ 8 + x mũ 7 + 1

X mũ 4 + 64

Answer 1

a, \(x^8+x^7+1\)

= \(x^7\left(x+1\right)+1\)

= \(x^7\left(x+1\right)+1+x-x\)

= \(x^7\left(x+1\right)+\left(x+1\right)-x\)

= \(\left(x^7+1\right)\left(x+1\right)-x\)

Answer 2

a) \(x^8+x^7+1\)

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

\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)

b) \(x^4+64\)

\(=\left(x^2+8\right)^2-16x^2\)

\(=\left(x^2+8+4x\right)\left(x^2+8-4x\right)\)