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\(4x^4+4x^3+5x^2+8x-6\)
\(=4x^4-2x^3+6x^3-3x^2+8x^2-4x+12x-6\)
\(=2x^3\left(2x-1\right)+3x^2\left(2x-1\right)+4x\left(2x-1\right)+6\left(2x-1\right)\)
\(=\left(2x^3+3x^2+4x+6\right)\left(2x-1\right)\)
\(=\left[x^2\left(2x+3\right)+2\left(2x+3\right)\right]\left(2x-1\right)\)
\(=\left(x^2+2\right)\left(2x+3\right)\left(2x-1\right)\)
\(4x^4+6x^3-4x^2+9x-15\)
\(=4x^4-4x^3+10x^3-10x^2+6x^2-6x+15x-15\)
\(=4x^3\left(x-1\right)+10x^2\left(x-1\right)+6x\left(x-1\right)+15\left(x-1\right)\)
\(=\left(4x^3+10x^2+6x+15\right)\left(x-1\right)\)
\(=\left[2x^2\left(2x+5\right)+3\left(2x+5\right)\right]\left(x-1\right)\)
\(=\left(2x^2+3\right)\left(2x+5\right)\left(x-1\right)\)
8x2 + 6x3 = 2x2( 4 + 3x )
4x2 - 10x3 = 2x2( 2 - 5x )
10x2 - 2x3 = 2x2( 5 - x )
21x + 7y = 7( 3x + y )
2x2 + 4x = 2x( x + 2 )
3x2 + 6x = 3x( x + 2 )
2x2 - 4x = 2x( x - 2 )
a) \(8x^2+6x^3=2x^2\left(4+3x\right)\)
b) \(4x^2-10x^3=2x^2\left(2-5x\right)\)
c) \(21x+7y=3\left(7x+y\right)\)
d) \(2x^2+4x=2x\left(x+2\right)\)
e) \(3x^2+6x=3x\left(x+2\right)\)
f) \(2x^2-4x=2x\left(x-2\right)\)
a) \(7x^3y-3xyz-21x^2+9z\)
\(=7x^2\left(xy-3\right)-3z\left(xy-3\right)\)
\(=\left(7x^2-3z\right)\left(xy-3\right)\)
b) \(4x^2-2x-y^2-y\)
\(=\left[\left(2x\right)^2-y^2\right]-\left(2x+y\right)\)
\(=\left(2x-y\right)\left(2x+y\right)-\left(2x+y\right)\)
\(=\left(2x+y\right)\left(2x-y-1\right)\)
c) \(9x^2-25y^2-6x+10y\)
\(=\left(3x\right)^2-\left(5y\right)^2-2\left(3x-5y\right)\)
\(=\left(3x-5y\right)\left(3x+5y\right)-2\left(3x-5y\right)\)
\(=\left(3x-5y\right)\left(3x+5y-2\right)\)
d) \(\left(5x-4\right)^2+\left(16-25x^2\right)+\left(5x-4\right)\left(3x+2\right)\)
\(=\left(5x-4\right)\left[\left(5x-4\right)+\left(3x+2\right)\right]+\left(4^2-\left(5x\right)^2\right)\)
\(=\left(5x-4\right)\left(8x-2\right)+\left(4-5x\right)\left(4+5x\right)\)
\(=\left(4-5x\right)\left(2-8x\right)+\left(4-5x\right)\left(4+5x\right)\)
\(=\left(4-5x\right)\left[\left(2-8x\right)+\left(4+5x\right)\right]\)
\(=\left(4-5x\right)\left(6-3x\right)\)