Question

factor completely.
(7q^2 - 35q - 98)

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of the terms \(7q^2\), \(-35q\), and \(-98\). The GCF of 7, 35, and 98 is 7. Factor out 7 from each term:
$$7q^2 - 35q - 98 = 7(q^2 - 5q - 14)$$

Step2: Factor the quadratic trinomial

Now, factor the quadratic trinomial \(q^2 - 5q - 14\). We need two numbers that multiply to \(-14\) and add up to \(-5\). The numbers are \(-7\) and \(2\) because \((-7) \times 2 = -14\) and \(-7 + 2 = -5\). So, we can factor \(q^2 - 5q - 14\) as \((q - 7)(q + 2)\).

Step3: Combine the factors

Putting it all together, the completely factored form is:
$$7(q - 7)(q + 2)$$

Answer:

\(7(q - 7)(q + 2)\)