Question

question
factor completely.
$18s^2 - 51s + 15$

Explanation:

Step1: Find the GCF

The coefficients are 18, -51, and 15. The GCF of 18, 51, and 15 is 3. Factor out 3:
$$18s^2 - 51s + 15 = 3(6s^2 - 17s + 5)$$

Step2: Factor the quadratic

We need two numbers that multiply to \(6\times5 = 30\) and add to -17. The numbers are -15 and -2. Rewrite the middle term:
$$6s^2 - 15s - 2s + 5$$
Group the terms:
$$(6s^2 - 15s) + (-2s + 5)$$
Factor out the GCF from each group:
$$3s(2s - 5) - 1(2s - 5)$$
Factor out \((2s - 5)\):
$$(3s - 1)(2s - 5)$$

Step3: Combine with the GCF

Putting it all together with the GCF from Step1:
$$3(3s - 1)(2s - 5)$$

Answer:

\(3(3s - 1)(2s - 5)\)