Factorize #x^2+6x-5#?

1 Answer
Mar 10, 2017

Answer:

Please see below.

Explanation:

As we have #x^2+6x# in the quadratic polynomial, it is akin to #(x+a)^2=x^2+2ax+a^2#. So we should convert the quadratic polynomial to this form. The process is explained below.

#x^2+6x-5#

= #x^2+2xx x xx3 +3^2 -3^2 -5#

= #(x+3)^2-9-5#

= #(x+3)^2-14#

Here it end the requirement of the question. But if what one wants is to factorize it, one can use #a^2-b^2=(a+b)(a-b)# and proceed as given below.

#(x+3)^2-14#

= #(x+3)^2-(sqrt14)^2#

= #(x+3+sqrt14)(x+3-sqrt14)#

Note: Had it been #x^2-6x# in the quadratic polynomial, we would have used #(x-a)^2=x^2-2ax+a^2#.