\(a.x^3+3x^2+4x+2\)

\(=x^3+x^2+2x^2+2x+2\)

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

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

\(b.6x^4-x^3-7x^2+x+1\)

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

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

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

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

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

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

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

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

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

k giùm cái cho đỡ buồn!

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

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

\(x^2-4x+4-y^2\)

\(=\left(x-2\right)^2-y^2\)

\(=\left(x-2-y\right)\left(x-2+y\right)\)

(x - 2)² - y² = (x - 2 - y)(x - 2 + y)

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

\(x^2-4x+4-y^2\)

\(=\left(x-2\right)^2-y^2\)

\(=\left(x-2-y\right)\left(x-2+y\right)\)

(x - 2)² - y² = (x - 2 - y)(x - 2 + y)

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

 4x^4 - 32x^2 +1 = 4x^4 + 4x^2 +1 - 36x^2 = (2x^2 + 1)^2 - 36x^2 = (2x^2 - 6x + 1)(2x^2 + 6x + 1) 

4 x⁴ - 32 x² + 1 

= ( 2 x² )² - 2 . 2x². 8 + 64 - 63 

= ( 2 x² - 8 )² - 63 

= ( 2x² - 8 + √63 ) ( 2x² - 8 - √63 )

Xong

Ta có:

\(x^3+2x^2+x+2\)

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

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

x³+2x²+x+2=x²(x+2)+(x+2)

                  =(x²+1)(x+2)

cam on ban nhieu lam

Viết đề rõ chút chứ nhìn ko ra

đề sai r nhé bạn, phải là  4x^4 - 32x^2 +1 mới đúng:

 4x^4 - 32x^2 +1 = 4x^4 + 4x^2 +1 - 36x^2 = (2x^2 + 1)^2 - 36x^2 = (2x^2 - 6x + 1)(2x^2 + 6x + 1) 

4⁴-32x²+1

=256-32x²+1

=-(32*x²-257)