Question

phân tích các đa thức sau thành nhân tử

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

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

c) \(x^5-x^4-1\)

d) \(x^7+x^5+1\)

e) \(x^8+x^4+1\)

giúp mk nha !!!

Answer 1

a).

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

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

d).

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

e).

\(x^8+x^4+1=x^8+2x^4+1-x^4\\ =\left(x^4+1\right)^2-\left(x^2\right)^2\\ =\left(x^4+x^2+1\right)\left(x^4-x^2+1\right)\\ =\left(x^4-x^2+1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)\)

Answer 2

c).

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

Answer 3

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

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

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

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

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

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

\(=x^8+x^7+x^6-x^6+1\)

\(=\left(x^8+x^7+x^6\right)-\left(x^6-1\right)\)

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

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

Answer 4

\(x^5+x+1\)

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

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

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

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

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