a: \(x^2+4x+3\)
\(=x^2+x+3x+3\)
=x(x+1)+3(x+1)
=(x+1)(x+3)
b: \(x^2-12x+32=x^2-4x-8x+32\)
=x(x-4)-8(x-4)
=(x-4)(x-8)
c: \(x^2-x-72=x^2-9x+8x-72\)
=x(x-9)+8(x-9)
=(x-9)(x+8)
d: \(2x^2-11x+5\)
\(=2x^2-10x-x+5\)
=2x(x-5)-(x-5)
=(x-5)(2x-1)
e: \(-x^2+2x+15\)
\(=-x^2+5x-3x+15\)
\(=-x\left(x-5\right)-3\left(x-5\right)=\left(x-5\right)\left(-x-3\right)\)
f: \(4x^2-4x-15\)
\(=4x^2-4x+1-16\)
\(=\left(2x-1\right)^2-16=\left(2x-1-4\right)\left(2x-1+4\right)\)
=(2x-5)(2x+3)
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