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c^{2}-4dc-21d^{2}
Consider c^{2}-4cd-21d^{2} as a polynomial over variable c.
\left(c-7d\right)\left(c+3d\right)
Find one factor of the form c^{k}+m, where c^{k} divides the monomial with the highest power c^{2} and m divides the constant factor -21d^{2}. One such factor is c-7d. Factor the polynomial by dividing it by this factor.