1. factorising this

$6(x-3)^2+13(x-3)+5$

2. Originally Posted by johnsy123
$6(x-3)^2+13(x-3)+5$
Use a dummy variable $X = x - 3$ so that the expression becomes

$6X^2 + 13X + 5$

$= 6X^2 + 3X + 10X + 5$

$= 3X(2X + 1) + 5(2X + 1)$

$= (2X + 1)(3X + 5)$

And since $X = x - 3$, this becomes

$[2(x - 3) + 1][3(x - 3) + 5]$

$= (2x - 6 + 1)(3x - 9 + 5)$

$= (2x - 5)(3x - 4)$.