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a)\(f\left(x\right)=\left(3x+4\right)\cdot\left(5x-1\right)+\left(5x+2\right)\cdot\left(1-3x\right)+2\)
\(=15x^2-3x+20x-4+5x-15x^2+2-6x+2\)
\(=16x\)
b)\(g\left(x\right)=\left(5x-1\right)\cdot\left(2x+3\right)-3\cdot\left(3x-1\right)\)
\(=10x^2+15x-2x-3-9x+3\)
\(=10x^2+4x\)
\(1,2x^3+3x^2-8x+3\)
\(=2x^3-2x^2+5x^2-5x-3x+3\)
\(=2x^2\left(x-1\right)+5x\left(x-1\right)-3\left(x-1\right)\)
\(=\left(2x^2+5x-3\right)\left(x-1\right)\)
\(=\left(2x-1\right)\left(x+3\right)\left(x-1\right)\)
\(2,x^3-5x^2+2x+8\)
\(=x^3+x^2-6x^2-6x+8x+8\)
\(=x^2\left(x+1\right)-6x\left(x+1\right)+8\left(x+1\right)\)
\(=\left(x^2-6x+8\right)\left(x+1\right)\)
\(=\left(x-2\right)\left(x-4\right)\left(x+1\right)\)
\(3,-6x^3+x^2+5x-2\)
\(=-6x^3-6x^2+7x^2+7x-2x-2\)
\(=-6x^2\left(x+1\right)+7x\left(x+1\right)-2\left(x+1\right)\)
\(=\left(-6x^2+7x-2\right)\left(x+1\right)\)
\(=\left(-6x^2-3x-4x-2\right)\left(x+1\right)\)
\(=\left[-3x\left(2x+1\right)-2\left(2x+1\right)\right]\left(x+1\right)\)
\(=\left(-3x-2\right)\left(2x+1\right)\left(x+1\right)\)
\(4,3x^3+19x^2+4x-12\)
\(=3x^3+18x^2+x^2+6x-2x-12\)
\(=3x^2\left(x+6\right)+x\left(x+6\right)-2\left(x+6\right)\)
\(=\left(3x^2+x-2\right)\left(x+6\right)\)
\(=\left(3x-2\right)\left(x+1\right)\left(x+6\right)\)