As we have x^2+6xx2+6x in the quadratic polynomial, it is akin to (x+a)^2=x^2+2ax+a^2(x+a)2=x2+2ax+a2. So we should convert the quadratic polynomial to this form. The process is explained below.
x^2+6x-5x2+6x−5
= x^2+2xx x xx3 +3^2 -3^2 -5x2+2×x×3+32−32−5
= (x+3)^2-9-5(x+3)2−9−5
= (x+3)^2-14(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)a2−b2=(a+b)(a−b) and proceed as given below.
(x+3)^2-14(x+3)2−14
= (x+3)^2-(sqrt14)^2(x+3)2−(√14)2
= (x+3+sqrt14)(x+3-sqrt14)(x+3+√14)(x+3−√14)
Note: Had it been x^2-6xx2−6x in the quadratic polynomial, we would have used (x-a)^2=x^2-2ax+a^2(x−a)2=x2−2ax+a2.
