a) Ta có: \(x^2-2x-15\)
\(=x^2-5x+3x-15\)
\(=x\left(x-5\right)+3\left(x-5\right)\)
\(=\left(x-5\right)\left(x+3\right)\)
b) Ta có: \(x^2-10x+24\)
\(=x^2-4x-6x+24\)
\(=x\left(x-4\right)-6\left(x-4\right)\)
\(=\left(x-4\right)\left(x-6\right)\)
c) Ta có: \(4x^2-5x+1\)
\(=4x^2-4x-x+1\)
\(=4x\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left(4x+1\right)\)
f) Ta có: \(\left(x+y\right)^2-25\left(x+y\right)+24\)
\(=\left(x+y\right)^2-\left(x+y\right)-24\left(x+y\right)+24\)
\(=\left(x+y\right)\left(x+y-1\right)-24\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left(x+y-24\right)\)
g) Ta có: \(x^5-5x^3+4\)
\(=x^5-x^3-4x^3+4\)
\(=x^3\left(x^2-1\right)-4\left(x^3-1\right)\)
\(=x^3\left(x-1\right)\left(x+1\right)-4\left(x-1\right)\left(x^2+x+1\right)\)
\(=\left(x-1\right)\left[x^3\left(x+1\right)-4\left(x^2+x+1\right)\right]\)
\(=\left(x-1\right)\left(x^4+x^3-4x^2-4x-4\right)\)