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2x^{2}+\left(2+a\right)x-24+4a
Consider 2x^{2}+2x-24+ax+4a as a polynomial over variable x.
\left(x+4\right)\left(2x+a-6\right)
Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 2x^{2} and n divides the constant factor 4a-24. One such factor is x+4. Factor the polynomial by dividing it by this factor.