5n^2 + 19n +12 How do I factor this trinomial step by step?

Question

5n^2 + 19n +12     How do I factor this trinomial step by step?

campbell_st · Answer

well there are a lot of different methods  

I use this as a fail-safe method

for a quadratic 

$$ax^2 + bx + c $$

multiply the coefficient of the leading term by the constant...  a x c

5 x 12 = 60

find the factors of 60 that add to 19

15, 4

I then have the 

$$\frac{(ax + factor1)(ax + fractor2)}{a}$$

in your question its 

$$\frac{(5x + 15)(5x + 4)}{5} $$

(5x + 15) can be written as 5(x + 3)

so you have 

$$\frac{5(x + 3)(5x + 4)}{5}$$

cancel the common factor of 5 from the numerator and denominator which gives

$$5x^2 + 19x + 12 = (x + 3)(5x + 4)$$

hope this helps