Home > College of Sciences > Maths First SEARCH MASSEY

# Factorization

## Exponential Functions

Two extra tricks need to be kept in mind when dealing with exponential functions.

enx = (ex)n

ea + b = (ea)(eb)

### Example 5

4xe2x ­ 8ex

Strategy

4xe2x and 8ex

Consider each product separately, but watch out for sums which may be in common

4 and 8 have a HCF of 4

Find the highest common factor of the numeric parts of the product expressions.

x is in only one term

Find the common factor for factors involving a variable.

Since e2x = (ex)2

e2x and ex have ex in common

Find the common factor for factors which involve exponential factors.

Hence 4ex is the largest common factor.

4xe2x ­ 8ex
= 4ex(xex) + 4ex(2)
= 4ex(xex + 2)

Put the parts together.

Here are some exercises to finish off:

### Exercise 5

1. ex + xex
2. e3x - e2x
3. 4ex + e4x
4. ey + 2 + e2y

 Contact Us | About Massey University | Sitemap | Disclaimer | Last updated: November 21, 2012     © Massey University 2003