Factorize x2+6x−5?

1 Answer
Shwetank Mauria
Mar 10, 2017

Please see below.

Explanation:

As we have x2+6x in the quadratic polynomial, it is akin to (x+a)2=x2+2ax+a2. So we should convert the quadratic polynomial to this form. The process is explained below.

x2+6x−5

= x2+2×x×3+32−32−5

= (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 a2−b2=(a+b)(a−b) and proceed as given below.

(x+3)2−14

= (x+3)2−(√14)2

= (x+3+√14)(x+3−√14)

Note: Had it been x2−6x in the quadratic polynomial, we would have used (x−a)2=x2−2ax+a2.

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