Exercise 5 Page 68

We want to completely factor the given expression. To do so, we will first identify and factor out the greatest common factor. The greatest common factor (GCF) of an expression is a common factor of the terms in the expression. It is the common factor with the greatest coefficient and the greatest exponent. The GCF of the given expression is 4. Note that expression in the parentheses has two terms.

x^2+16 First, note that there is no further greatest common factor. There are three additional common factoring techniques for binomials.

1. Difference of Two Squares
2. Difference of Two Cubes
3. Sum of Two Cubes

Both terms are squares, but they cannot be written as difference. This means that we cannot use the difference of two squares. Since neither term is a cube, we cannot use the sum or the difference of two cubes. Therefore, the given polynomial cannot be further factored. 4(x^2+16)

Extra

Factoring Techniques

Different factoring techniques can be applied according to the number of terms the polynomial has.

Number of Terms	Factoring Technique
Any number	Greatest Common Factor (GCF)
Two	Difference of Two Squares, Sum of Two Cubes, or Difference of Two Cubes
Three	Perfect Square Trinomials, or General Trinomials
Four or more	Grouping