Factorize each of the following quadratic polynomials by using the method of completing the square:
(1) `x^2+12 x+20`
(2) `a^2-14 a-51`

Explanation

By using the method of completing the square:
(1) `x^2+12 x+20`
`=x^2+12x+20`
`=x^2+12x+36-16`
`=(x+6)^2-4^2` .................(Completing the square)
By using the formula `(a^2-b^2)=(a+b)(a-b)`
`= (x+6+4)(x+6-4)`
`=(x+2)(x+10)`

(2) `a^2-14 a-51`
`=a^2-14a-51`
`=a^2-14a+49-100`
`=(a-7)^2-10^2` ................(Completing the square)
By using the formula `(a^2-b^2)=(a+b)(a-b)`
`=(a-7+10)(a-7-10)`
`=(a-17)(a+3)`