Answer:
(5m+4)(m+3)
Explanation:
Given the quadratic expression:
[tex]5m^2+19m+12[/tex]To factor the quadratic expression, follow the steps below:
Step 1: Multiply the coefficient of m² and the constant.
[tex]5\times12=60[/tex]Step 2: Find two numbers that multiply to give 60, and add to give the coefficient of m, 19 To do this, list the factors of 60: 1,2,3,4,6,10,15,20,30, and 60.
[tex]\begin{gathered} 15\times4=60 \\ 15+4=19 \end{gathered}[/tex]Step 3: Rewrite the middle term with those numbers.
[tex]=5m^2+15m+4m+12[/tex]Step 4: Factor the first two and last two terms separately. Ensure that the expression in the brackets is the same.
[tex]\begin{gathered} =5m(m+3)+4(m+3) \\ =(5m+4)(m+3) \end{gathered}[/tex]The factored form of the expression is:
[tex]\begin{equation*} (5m+4)(m+3) \end{equation*}[/tex]