a) x3 + 4x2 – 2x – 8

= (x3 + 4x2) - (2x + 8)

= x2(x + 4) - 2(x + 4)

= (x + 4)(x2 - 2)

= (x + 4)(x + √2)(x - √2)

\(2x+8=2\left(x+4\right)\)

\(=2\left(x+4\right)\)

\(\text{ 2x² + 6x - 8 }\)

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

a) \(\left(2x+5\right)^2-8^2\)

\(=\left(2x+5-8\right)\left(2x+5+8\right)\)

\(=\left(2x-3\right)\left(2x+13\right)\)

b) \(\left(2x-1\right)^2-\left(3x-1\right)^2\)

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

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

\(=-x\left(5x-2\right)\)

\(-8x^3+1=1^3-\left(2x\right)^3=\left(1-2x\right)\left(1+2x+4x^2\right)\)

a: \(x^4-2x^3+x^2-2x\)

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

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

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

b: \(x^4+x^3-8x-8\)

\(=\left(x^4+x^3\right)-\left(8x+8\right)\)

\(=x^3\left(x+1\right)-8\left(x+1\right)\)

\(=\left(x+1\right)\left(x^3-8\right)\)

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

\(A=x^8-2x^4-8\)

\(A=x^8-2x^4+4x^4-8\)

\(A=x^4\left(x^4-2\right)-4\left(x^4-2\right)\)

\(A=\left(x^4-4\right)\left(x^4-2\right)\)

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

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

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

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

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

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

Bạn cũng có thể đặt \(t=x^4\)để bài toán dễ làm hơn

a: \(x^4+x^2+2x+6\)

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

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