Question

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

Answer 1

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`.