The document provides instructions on how to completely factor polynomials. It gives examples of factoring expressions like 4n^2 - 16, 5x^2 - 45, and 3x^2 - 18x - 21. The steps explained are to find the greatest common factor, factor any binomials or trinomials, and simplify the expression as much as possible. Additional practice problems and their factored solutions are provided.

1. Factoring Polynomials
Completely
By L.D.

2. Problem 1
Instructions: Factor 4n2 – 16 completely.

3. Problem 1
Instructions: Factor 4n2 – 16 completely.
The first thing we need to do here is to find the GCF
and make the problem look like 4(n2 – 4)

4. Problem 1
Instructions: Factor 4n2 – 16 completely.
The first thing we need to do here is to find the GCF
and make the problem look like 4(n2 – 4)
The next thing we need to do is to factor the binomial
inside, n2 – 4 will become (n + 2)(n - 2).

5. Problem 1
Instructions: Factor 4n2 – 16 completely.
The first thing we need to do here is to find the GCF
and make the problem look like 4(n2 – 4)
The next thing we need to do is to factor the binomial
inside, n2 – 4 will become (n + 2)(n - 2).
The last thing to be done is that the problem will end
up 4(n + 2)(n - 2) which is factored as far as we can
take it.

6. Problem 1 Extras
Factor These Completely:
- 5x2 - 45
- 4 – 30
- 8x2 + 64

7. Problem 1 Extras
Factor These Completely:
- 5x2 – 45 5(x + 3)(x – 3)
- 8d3 + 24d 4d(2d2 + 6)
- 8x2 + 64

8. Problem 2
Instructions: Factor 9y3 + 81y2 = 0 completely and
solve

9. Problem 3
Instructions: Factor 3x2 – 18x – 21 completely.

10. Problem 3
Instructions: Factor 3x2 – 18x – 21 completely.
First, find the GCF to get 3(x2 – 6x – 7)

11. Problem 3
Instructions: Factor 3x2 – 18x – 21 completely.
First, find the GCF to get 3(x2 – 6x – 7)
Now, you need to factor the interior to get (x + 7)(x –
1), making our answer 3(x + 7)(x – 1).