Question

[Nguyễn Thế Phúc Anh]

Phân tích các đa thức sau thành nhân tử:

a, x⁴ + 1996.x² + 1995.x + 1996

b, x⁴ + 1997.x² + 1996.x + 1997

Answer 1

[nam do]

a)

\(x^4+1996x^2+1995x+1996\)

\(=\left(x^4-x\right)+\left(1996x^2+1996x+1996\right)\)

\(=x\left(x^3-1\right)+1996\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+1996\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left[x\left(x-1\right)+1996\right]\)

\(=\left(x^2+x+1\right)\left(x^2-x+1996\right)\)

b)

\(x^4+1997x^2+1996x+1997\)

\(=\left(x^4-x\right)+\left(1997x^2+1997x+1997\right)\)

\(=x\left(x^3-1\right)+1997\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+1997\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left[x\left(x-1\right)+1997\right]\)

\(=\left(x^2+x+1\right)\left(x^2-x+1997\right)\)

Answer 2

[Nguyễn Thị Hằng]

x⁴+1996x²+1995x+1996

=(x^4_x)+(1996x²+1996x+1996)

=x(x³-1)+1996(x²+x+1)

=x(x-1)(x²+x+1)+1996(x²+x+1)

=(x²+x+1)((x²-1)+1996)

=(x²+x+1)((x+1)(x-1)+1996)

Câu 2 tương tự bạn nhé!