\(\left(x^2+x+1\right)\left(x^2+x+5\right)-21=x^4+x^3+5x^2+x^3+x^2+5x+x^2+x+5-21=x^4+2x^3+7x^2+6x-16=\left(x-1\right)\left(x+2\right)\left(x^2+x+8\right)\)

\(=\left(x^2+x+1\right)\left(x^2+x+1+4\right)-21\)

\(=\left(x^2+x+1\right)^2+4\left(x^2+x+1\right)-21\)

\(=\left(x^2+x+1\right)^2-3\left(x^2+x+1\right)+7\left(x^2+x+1\right)-21\)

\(=\left(x^2+x+1\right)\left(x^2+x-2\right)+7\left(x^2+x-2\right)\)

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

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

x2 - x = x.x - x.1 = x(x - 1)

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

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

x2 – x – 6

= x2 + 2x – 3x – 6

(Tách –x = 2x – 3x)

= x(x + 2) – 3(x + 2)

(có x + 2 là nhân tử chung)

= (x – 3)(x + 2)

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

\(\Leftrightarrow x^2\left(x-2\right)+x\left(x-2\right)+\left(x-2\right)\)

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

Ai đồ giỏi Toán quasss cho em xin víaaa.

-Đặt \(t=\left(x^2-x+1\right)\)

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

\(=t^2-5xt+4x^2\)

\(=t^2-4xt-xt+4x^2\)

\(=t\left(t-4x\right)-x\left(t-4x\right)\)

\(=\left(t-4x\right)\left(t-x\right)\)

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

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

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

CAM ON - HOANG

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

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

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

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