Question

factorise
$15 {x}^{2} + 16x + 3$

Answer 1

   15x² + 16x + 3

= [ (√15 x )² + 2(√15 x)(8/√15) + (8/√15)² ]  -(8/√15)² + 3

= (√15 x + 8/√15)²  - 64/15 + 3

(apply formula  a² + b ² + 2ab = (a+b)² )

=   (√15 x + 8/√15)²  -64+45/15)

= (√15 x + 8/√15)² - 19/15)

= (√15 x + 8/√15)² - (√19/√15)²

(use formula a²-b² = (a+b) (a-b))

= (√15 x + 8/√15 + √19/√15) (√15 x + 8√15 - √19/√15)

= ( √15 x + (8+√19)/√15) ( √15 x + (8-√19)/√15)


Hope it is helfful for you # thank you