Question

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

Answer 1

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