Question

Factorize each of the following algebraic expression:
a² − 14a − 51

Answer 1

$$\begin{gathered} \mathrm{To}\mathrm{factorise}{\mathrm{a}}^2-14\mathrm{a}-51,\mathrm{we}\mathrm{will}\mathrm{find}\mathrm{two}\mathrm{numbers}\mathrm{p}\mathrm{and}\mathrm{q}\mathrm{such}\mathrm{that}\mathrm{p}+\mathrm{q}=-14\mathrm{and}\mathrm{pq}=-51. \\ \mathrm{Now}, \\ 3+(-17)=-14 \\ \mathrm{and} \\ 3\times (-17)=-51 \\ \mathrm{Splitting}\mathrm{the}\mathrm{middle}\mathrm{term}-14\mathrm{a}\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{quadratic}\mathrm{as}3\mathrm{a}-17\mathrm{a},\mathrm{we}\mathrm{get}: \\ {\mathrm{a}}^2-14\mathrm{a}-51={\mathrm{a}}^2+3\mathrm{a}-17\mathrm{a}-51 \\ =({\mathrm{a}}^2+3\mathrm{a})-(17\mathrm{a}+51) \\ =\mathrm{a}(\mathrm{a}+3)-17(\mathrm{a}+3) \\ =(\mathrm{a}-17)(\mathrm{a}+3) \end{gathered}$$