(x + 3 )(2x + 5)
consider the factors of the product of the coefficient of the x² term and the constant which sum to give the coefficient of the x term
consider the factors of the product 2 × 15 = 30 which sum to give + 11
these are + 6 and + 5
split the middle term using these factors
2x² + 6x + 5x + 15 ( factor by grouping )
= 2x(x + 3 ) + 5(x + 3 ) ( factor out (x + 3) )
= (x + 3)(2x + 5) ← in factored form