Question

phân tích đa thức thành nhân tử

x^4+x^3+x+1

x^4-x^3-x^2-1

Answer 1

x⁴+x³+x+1

=x³(x+1)+(x+1)

=(x³+1)(x+1)

=(x+1)(x²-x+1)(x+1)

=(x+1)²(x²-x+1)

Answer 2

x⁴ + x³ + x +1 = x³ ( x + 1) + ( x + 1).1

= ( x+1)(x³+ 1)

Answer 3

\(x^4-x^3-x^2-1\)

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

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

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

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