Factorize each of the following quadratic polynomials by using the method of completing the square:
(1) `y^2-7y+12`
(2) `z^2-4z-12`

Explanation

By using the method of completing the square:
(1) `y^2-7y+12`
`y^2-7y+12`
`=y^2-7y+(7/2)^2-(7/2)^2+12` .........[Adding and subtracting `(7/2)^2`]
`=(y-7/2)^2-(7/2)^2`..........(Completing the square)
By using the formula `(a^2-b2)=(a+b)(a-b)`
`=(y-(7/2-1/2))(y-(7/2+1/2))`
`=(y-3)(y-4)`

(2) `z^2-4z-12`
`=z^2-4z-12=z^2-4z+4-16`
`=(z-2)^2-4^2` ....................(Completing the square)
By using the formula `(a^2-b^2)=(a+b)(a-b)`
`=(z-2+4)(z-2-4)`
`=(z-6)(z+2)`