How do you factor completely # x^2 + 8x+ 12#?

1 Answer
May 27, 2016

Answer:

#x=-2# or #x=-6#

Explanation:

To solve #x^2+8x+12=0#, we should first factorize the polynomial #x^2+8x+12#

To factorize a quadratic polynomial of type #ax^2+bx+c#,

one needs to split middle term #b# in two parts whose product is #ac#. As in #x^2+8x+12#, the product is #1*12=12# and middle term #8#, it can be split in #6# and #2#.

Hence, #x^2+8x+12=0# can be written as

#x^2+6x+2x+12=0#

or #x(x+6)+2(x+6)=0#

or #(x+2)(x+6)=0#

Hence, either #x+2=0# or #x+6=0# i.e.

#x=-2# or #x=-6#