How do you factor 2r^2 + 5r + 3

Magic and experience and trial and error

use ac method

2 times 3=6

what 2 numbers multiply to get 6 and add to get 5?, 2 and 3

split the middle number into those

2r²+2r+3r+3

group

(2r²+2r) + (3r+3)

factor

2r (r+1) + 3 (r+1)

undistribute

(r+1) (2r+3)