Question

1. $14x^2 - 92x - 42$

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of the coefficients 14, -92, and -42. The GCF of 14, 92, and 42 is 2. So we factor out 2:
$$14x^2 - 92x - 42 = 2(7x^2 - 46x - 21)$$

Step2: Factor the quadratic trinomial

Now we need to factor \(7x^2 - 46x - 21\). We look for two numbers that multiply to \(7\times(-21)= -147\) and add up to -46. After some trial and error, we find that -49 and 3 work because \(-49\times3 = -147\) and \(-49 + 3 = -46\). We rewrite the middle term using these numbers:
$$7x^2 - 49x + 3x - 21$$

Step3: Group and factor

Group the first two terms and the last two terms:
$$(7x^2 - 49x) + (3x - 21)$$
Factor out the GCF from each group:
$$7x(x - 7) + 3(x - 7)$$
Now we can factor out \((x - 7)\):
$$(7x + 3)(x - 7)$$

Step4: Combine with the GCF

Remember we factored out a 2 in Step 1, so the fully factored form is:
$$2(7x + 3)(x - 7)$$

Answer:

\(2(7x + 3)(x - 7)\)