\(4\left(x^2+15x+50\right)\left(x^2+18x+72\right)-3x^2\\ =4\left(x+5\right)\left(x+10\right)\left(x+6\right)\left(x+12\right)-3x^2\\ =4\left(x^2+16x+60\right)\left(x^2+17x+60\right)-3x^2\)

Đặt \(x^2+16x+60=a\)

\(=4a\left(a+x\right)-3x^2\\ =4a^2+4ax-3x^2\\ =\left(2a-x\right)\left(2a+3x\right)\\ =\left[2\left(x^2+16x+60\right)-x\right]\left[2\left(x^2+16x+60\right)+3x\right]\\ =\left(2x^2+31x+120\right)\left(2x^2+35x+120\right)\)

Đặt 

\(\left(x^2+5x-3\right)\left(x^2+5x-5\right)-15=\left(x^2+5x-3\right)\left(x^2+5x-3-2\right)-15=\left(x^2+5x-3\right)^2-2\left(x^2+5x-3\right)+1-16=\left(x^2+5x-3-1\right)^2-4^2=\left(x^2+5x-4\right)^2-4^2=\left(x^2+5x-8\right)\left(x^2+5x\right)=x\left(x+5\right)\left(x^2+5x-8\right)\)

\(\left(x^2+5x-3\right)\left(x^2+5x-5\right)-15\)

\(=\left(x^2+5x\right)^2-8\left(x^2+5x\right)-15\)

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

-x² - 5x + 24

= -x² + 3x - 8x + 24

= -x(x + 3) - 8(x - 3)

= (-x - 8)(x + 3)

=(3x-x²)+(24-8x)=3x(1-x)+8(1-x)=(1-x)(3x+8)

\(-x^2-5x+24\)

\(=-x^2-8x+3x+24\)

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

=3x(x+2y)

=3x(x+2y)

3x² + 6xy

= 3x(x+2y)

\(3x^2-14x-5=3x\left(x-5\right)+\left(x-5\right)=\left(x-5\right)\left(3x+1\right)\)

\(3x^2-14x-5\)

\(=3x^2-15x+x-5\)

\(=3x\left(x-5\right)+x-5\)

\(=\left(x-5\right)\left(3x+1\right)\)

A= 3x^2 + 14x - 15
3A= (3x)^2 + 2.7.(3x) - 15.3
3A= (3x+7)^2 +(15.3-7.7)
3A= (3x+7 )^2 -2^2
3A= (3x+7-2 )((3x+7+2 )
A= ( 3x-5)( x+ 3)

Đa thức này không phân tích được thành nhân tử

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

\(15x^3y^2+10x^2y^2-2x^2y^3\)

\(=x^2y^2\left(15x+10-2y\right)\)

`15x^3 y^2 + 10x^2 y^2 - 2x^2 y^3`

`=x^2y^2(15x+10-2y)`

=5(x²-9)

=5(x²-3²)

=5(x-3)(x+3)