Question

1. \\(28n^4 + 16n^3 - 80n^2\\)

Explanation:

Identify the terms

We start with the polynomial:

$$28n^4 + 16n^3 - 80n^2$$

Find the GCF of coefficients

Find the greatest common factor of \(28\), \(16\), and \(-80\).
The factors of each are:

• \(28 = 4 \times 7\)
• \(16 = 4 \times 4\)
• \(-80 = 4 \times (-20)\)

The greatest common numerical factor is \(4\).

Find the GCF of variables

Find the lowest power of \(n\) in the terms:

• \(n^4\)
• \(n^3\)
• \(n^2\)

The lowest power is \(n^2\).

Factor out the GCF

Combine the GCF of coefficients and variables:

$$\text{GCF} = 4n^2$$

Divide each term by \(4n^2\):

• \(\frac{28n^4}{4n^2} = 7n^2\)
• \(\frac{16n^3}{4n^2} = 4n\)
• \(\frac{-80n^2}{4n^2} = -20\)

Write the factored expression

Combine the GCF and the remaining terms:

$$4n^2(7n^2 + 4n - 20)$$

The quadratic inside cannot be factored further over the integers.

Answer:

\(4n^2(7n^2 + 4n - 20)\)