Multiplying Linear Functions

Multiply the following two linear functions:

(x+3)(2x+5)

Answer :




Explanation: The standard format of a Linear Function is as follows: f(x) = ax + b

It is important to keep in mind the following regarding Linear Functions:

1. The term “Linear” is derived from the word “Line”. Therefore a Linear Function is a function or equation of a straight line.

2. The degree of this function is always 1 (a degree means the highest power or exponent The variable in the function is raised to.

Therefore by looking at the two sets of functions presented in this problem we can identify (x+3) as one linear function and also (2x+5) as another linear function and the requirement of this problem is to multiply the two and end up with a resulting quadratic equation.

In order to perform the multiplication we use a method called FOIL which stands for:

First – Outer – Inner – Last

Lets now identify those terms in the above linear functions:

First terms : (x) in the first function (x+3) and the (2x) in the (2x+5) function

Outer terms : (x) in the first function (x+3) and the (5) in the (2x+5) function

Inner terms : (3) in the first function (x+3) and the (2x) in the (2x+5) function

Last terms : (3) in the first function (x+3) and the (5) in the (2x+5) function

Now let us implement the above multiplication:






Notice that the middle like terms of 5x and 6x are combined and thus results in 11x as the middle term for the resulting quadratic function.

© Copyright 2012 Najwa S. Hirn. All rights reserved.