The factored form is $$ \color{blue}{ 3x^2+5x+2 = \left(3x+2\right)\left(x+1\right) } $$

** Step 1:** **Identify constants $ a $ , $ b $ and $ c $.**

$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:

** Step 2:** Multiply the leading coefficient $\color{blue}{ a = 3 }$ by
the constant term $\color{blue}{c = 2} $.

** Step 3:** Find out two numbers that multiply to $ a \cdot c = 6 $ and add to $ b = 5 $.

** Step 4:** All pairs of numbers with a product of $ 6 $ are:

PRODUCT = 6 | |

1 6 | -1 -6 |

2 3 | -2 -3 |

** Step 5:** Find out which factor pair sums up to $\color{blue}{ b = 5 }$

PRODUCT = 6 and SUM = 5 | |

1 6 | -1 -6 |

2 3 | -2 -3 |

** Step 6:** Replace middle term $ 5 x $ with $ 3x+2x $:

** Step 7:** Apply factoring by grouping. Factor $ 3x $ out of the first two terms
and $ 2 $ out of the last two terms.

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