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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

Factorise these then check your answers.

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

 

<< Trigonometric Functions | Factorisation Index | Quadratic Functions >>

 

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