a.
Đặt \(x^2+x=a\)
\(a^2-14a+24=a^2-2a-12a+24=a\left(a-2\right)-12\left(a-2\right)\)
\(=\left(a-12\right)\left(a-2\right)=\left(x^2+x-12\right)\left(x^2+x-2\right)\)
\(=\left(x-3\right)\left(x+4\right)\left(x-1\right)\left(x+2\right)\)
c.
\(x^4+2x^3+5x^2+4x-12=\left(x^4+2x^3+x^2\right)+4\left(x^2+x\right)-12\)
\(=\left(x^2+x\right)^2+4\left(x^2+x\right)-12\)
Đặt \(x^2+x=a\)
\(a^2+4a-12=a^2+6a-2a-12=a\left(a+6\right)-2\left(a+6\right)\)
\(=\left(a-2\right)\left(a+6\right)=\left(x^2+x-2\right)\left(x^2+x+6\right)\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)
e.
\(\left(x+1\right)\left(x+7\right)\left(x+3\right)\left(x+5\right)+15\)
\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)
Đặt \(x^2+8x+7=a\)
\(a\left(a+8\right)+15=a^2+8a+15=a^2+3a+5a+15\)
\(=a\left(a+3\right)+5\left(a+3\right)=\left(a+3\right)\left(a+5\right)\)
\(=\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)
\(=\left(x+2\right)\left(x+6\right)\left(x^2+8x+10\right)\)
