Question

1. $6x^2 + 3x - 84$

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of \(6x^2\), \(3x\), and \(-84\). The GCF of 6, 3, and 84 is 3. So we factor out 3:
\(6x^2 + 3x - 84 = 3(2x^2 + x - 28)\)

Step2: Factor the quadratic

Now we need to factor the quadratic \(2x^2 + x - 28\). We look for two numbers that multiply to \(2 \times (-28) = -56\) and add up to 1. The numbers are 8 and -7.
Rewrite the middle term using these numbers:
\(2x^2 + 8x - 7x - 28\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((2x^2 + 8x) + (-7x - 28)\)
Factor out the GCF from each group:
\(2x(x + 4) - 7(x + 4)\)

Step4: Factor out the common binomial

Now we can factor out the common binomial \((x + 4)\):
\((2x - 7)(x + 4)\)

Step5: Combine with the GCF

Putting it all together with the GCF we factored out earlier:
\(3(2x - 7)(x + 4)\)

Answer:

\(3(2x - 7)(x + 4)\)