$$ \definecolor{crimBlue}{rgb}{0.196,0.467,0.533} \definecolor{crimOrange}{rgb}{0.969,0.553,0.149} \definecolor{crimGreen}{rgb}{0.498,0.694,0.302} $$
Complete the steps to factor $#2x^2 + 6x + 5x + 15$# by grouping.

Step 1: Group the first two terms and the second two terms.

Step 2: What is the greatest common factor of Group 1?
$#2$#
$#x$#
$#2x$#

Step 3: What is the greatest common factor of Group 2?
$#3$#
$#5$#
$#5x$#

Step 4: What is the common factor in both terms of the resulting expression?
$#2x$#
$#3$#
$#x + 3$#

Step 5: Use the distributive property to write the factored form of the polynomial.
$#(x + 3)(2x + 5)$#
$#(2x + 3)(x + 5)$#

$#2x^2 + 6x + 5x + 15$#
$#= (2x^2 + 6x)$#
    Group 1
  +  $#(5x + 15)$#
      Group 2


$$= 2x(x+3) + (5x + 15)$$
$$= 2x(x+3) + 5(x + 3)$$
$$= 2x\enclose{circle}[mathcolor="red"]{(x + 3)} + 5\enclose{circle}[mathcolor="red"]{(x + 3)}$$
$$ = (x + 3)(2x + 5)$$