(1) `x^2+10x+24`

The coefficients are `a=1,b=10,c=24`

Find pair of factors whose product is `a*c=1 * 24=24` and sum is `b=10`

The pairs of factors for 24 and their sums are
`1,24 : 1+24=25`

`2,12 : 2+12=14`

`3,8 : 3+8=11`

`4,6 : 4+6=10`

Factors are `4,6` whose product is `4 * 6=24` and sum is `4+6=10`

So use `4` and `6` to split the `10` coefficient on the middle term

`=x^2+4x+6x+24`

`=x(x+4)+6(x+4)`

`=(x+4)(x+6)`