Question 417682
{{{2n^2+5n-42)}}}
We multiply {{{-42*2=84}}}
We try to find two numbers having sum 5 and product 84,that is
select from the factors of -84
-1*84
-2*42
-3*28
-4*21
-6*14
-7*12 etc.
Since -7+12=5 we stop here this search of number pairs and we have
{{{2n^2+(-7+12)n-42)}}}=
{{{2n^2-7n+12n-42}}}=
{{{n(2n-7)+6(2n-7)}}}=
{{{(2n-7)(n+6)}}}

For the other expression
{{{5x^2+35x+30}}}=
{{{5(x^2+7x+6)}}}
1*6
2*3
3*2
etc.... stop... we found {{{1*6=6}}} and {{{1+6=7}}}
going back to the expression we obtain:
{{{5(x^2+(1+6)x+6)}}}=
{{{5(x^2+x+6x+6)}}}=
{{{5(x(x+1)+6(x+1))}}}=
{{{5(x+1)(x+6)}}}