Question

Factor 5m² + 19m + 12.

Answer 1

(5m+4)(m+3)

Explanation:

Given the quadratic expression:

`5m^2+19m+12`

To factor the quadratic expression, follow the steps below:

Step 1: Multiply the coefficient of m² and the constant.

`5*12=60`

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.

`\begin{gathered} 15*4=60 \\ 15+4=19 \end{gathered}`

Step 3: Rewrite the middle term with those numbers.

`=5m^2+15m+4m+12`

Step 4: Factor the first two and last two terms separately. Ensure that the expression in the brackets is the same.

`\begin{gathered} =5m(m+3)+4(m+3) \\ =(5m+4)(m+3) \end{gathered}`

The factored form of the expression is:

`\begin{equation*} (5m+4)(m+3) \end{equation*}`