2x+3 is a factor of 2x³+5x²-37x-60
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let p(x)= 2x^3+5x^2-37x-60
if 2x+3 is a factor
we have to show that p(-3/2)=0
p(-3/2)= 2*(-3/2)^3+5*(-3/2)^2-37*(-3/2)-60
=2*(-27/8)+5*9/4+111/2-60
=--27/4+45/4+111/2-60/1
=(-27+45+222-240)/4
=(-249+285)/4
=36/4
=9
hence p(-3/2) is not equal to zero
therefore
2x+3 is not a factor of p(x)
if 2x+3 is a factor
we have to show that p(-3/2)=0
p(-3/2)= 2*(-3/2)^3+5*(-3/2)^2-37*(-3/2)-60
=2*(-27/8)+5*9/4+111/2-60
=--27/4+45/4+111/2-60/1
=(-27+45+222-240)/4
=(-249+285)/4
=36/4
=9
hence p(-3/2) is not equal to zero
therefore
2x+3 is not a factor of p(x)
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