Question

factor completely.
12s² + 54s - 66

Explanation:

Step1: Find GCF of coefficients

The coefficients are 12, 54, -66. GCF of 12, 54, 66 is 6.
$$12s^2 + 54s - 66 = 6(2s^2 + 9s - 11)$$

Step2: Factor quadratic trinomial

Factor \(2s^2 + 9s - 11\). Find two numbers \(a,b\) such that \(a\times b = 2\times(-11)= -22\) and \(a + b = 9\). The numbers are 11 and -2.
Rewrite middle term: \(2s^2 + 11s - 2s - 11\)
Group and factor: \((2s^2 + 11s) - (2s + 11) = s(2s + 11) - 1(2s + 11) = (2s + 11)(s - 1)\)

Step3: Combine with GCF

Putting it all together: \(6(2s + 11)(s - 1)\)

Answer:

\(6(2s + 11)(s - 1)\)