Question

example 4: $12c^{2}+11c-5$
$c^{2}+11c-60$

Explanation:

Step1: Factor $12c^2+11c-5$

Find two numbers: product $12\times(-5)=-60$, sum $11$. The numbers are $15$ and $-4$.
Rewrite and factor:

$$\begin{align*} 12c^2+15c-4c-5&=3c(4c+5)-1(4c+5)\\ &=(3c-1)(4c+5) \end{align*}$$

Step2: Factor $c^2+11c-60$

Find two numbers: product $-60$, sum $11$. The numbers are $15$ and $-4$.
Factor directly:
$$(c+15)(c-4)$$

Answer:

$12c^2+11c-5=(3c-1)(4c+5)$
$c^2+11c-60=(c+15)(c-4)$