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

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

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

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

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

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

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

Cái này đã là nhân tử rồi mà bạn

\(5x^2-4\left(x^2-2x+1\right)-5=\left(5x^2-5\right)-4\left(x-1\right)^2=5\left(x^2-1\right)-4\left(x-1\right)^2=5\left(x-1\right)\left(x+1\right)-4\left(x-1\right)^2=\left(x-1\right)\left[5\left(x+1\right)-4\left(x-1\right)\right]=\left(x-1\right)\left(5x+5-4x+4\right)=\left(x-1\right)\left(x+9\right)\)

\(= \)\(5x^2-4x^2+8x-4-5\)

\(=\)\(x^2+8x-9\)

\(=x^2+9x-x-9\)

\(=(x-1)(x+9)\)

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

\(=5x^2-4x^2+8x-4-5\)

\(=x^2+8x-9\)

\(=\left(x+9\right)\left(x-1\right)\)

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

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

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

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

x^4+x^3+2x^2+x+1

=(x^4+2x^2+1)+(x^3+x)

=(x^2+1)^2+x(x^2+1)

=(x^2+1)(x^2+x+1)

a)\(5x^2-4\left(x^2-2x+1\right)-5=5\left(x^2-1\right)-4\left(x-1\right)^2=5\left(x-1\right)\left(x+1\right)-4\left(x-1\right)^2=\left(x-1\right)\left(5x+5-4x+4\right)=\left(x-1\right)\left(x+9\right)\)

b) \(9x^2+6x-4y^2+4y=\left(9x^2+6x+1\right)-\left(4y^2-4y+1\right)=\left(3x+1\right)^2-\left(2y-1\right)^2=\left(3x+1-2y+1\right)\left(3x+1+2y-1\right)=\left(3x-2y+2\right)\left(3x+2y\right)\)

a: \(5x^2-4\left(x^2-2x+1\right)-5\)

\(=5x^2-4x^2+8x-4-5\)

\(=x^2+8x-9\)

\(=\left(x+9\right)\left(x-1\right)\)

b: \(9x^2+6x-4y^2+4y\)

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

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

\(x^2-2x-24\)

\(=x^2-6x+4x-24\)

\(=x(x-6)+4(x-6)\)

\(=(x+4)(x-6)\)

\(x^2-2x-24\\ =x^2-2x+1-25\\ =\left(x-1\right)^2-5^2\\ =\left(x-1-5\right)\left(x-1+5\right)\\ =\left(x-6\right)\left(x+4\right)\)

\(x^2-2x-24=\left(x-6\right)\left(x+4\right)\)

\(\left(x^2-2x-6\right)\left(x^2-2x-11\right)+6\)

\(=\left(x^2-2x\right)^2-17\left(x^2-2x\right)+66+6\)

\(=\left(x^2-2x\right)^2-17\left(x^2-2x\right)+72\)

\(=\left(x^2-2x-8\right)\left(x^2-2x-9\right)\)

\(=\left(x-4\right)\left(x+2\right)\left(x^2-2x-9\right)\)

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

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

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

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

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

a)  x^6 - x^4 + 2x^3 + 2x^2 

=x²(x⁴-x²+2x+2)

=x²[x⁴-2x³+2x²+2x³-4x²+4x+x²-2x+2]

=x²[x²(x²-2x+2)+2x(x²-2x+2)+(x²-2x+2)

=x²[(x²+2x+1²)(x²-2x+2)]

=x²(x+1)²(x²-2x+2)

b) x^(m+4) + x^(m+1) - x - 1

Ta thấy x=-1 là nghiệm của đa thức

=>đa thức có 1 hạng tử là x+1

=>đa thức đc phân tích là

=(x+1)(x^m+3-x^m+2+x^m+1-1)