2. Give an example of each of the following.
b. A repeat...

Question

2. Give an example of each of the following.

b. A repeated linear factor

Accepted Answer

Welcome back, everyone. Which of the following rational expressions contains a repeated linear factor in the denominator? In this problem, we have 4 options to consider, and in order to solve it, we can remember that a linear factor will have a form of MX + B. That's the general expression of a linear factor, and if it is repeated, we can just say that it's going to be multiplied by itself at least one time, right? So we can write MX + B, raise to the power of N where N is greater than or equal to 2, and N is an integer. In other words, a repeated linear factor will be a square, a cube, and so on of a linear form MX plus B. Starting with option A, we can focus on our denominator, which is X + 1 squared. This matches our definition. We have a linear factor X + 1, and it is squared, right? So we can write X + 1 multiplied by X + 1. Our linear factor is X + 1 and it is repeated twice, meaning A is the correct option. Now let's consider the remaining options. Option B contains X2 + 1. Notice that this is an irreducible factor, right? So we can say it is irreducible. Because we cannot factor it out and we cannot get linear factors out of this form of X2 + 1 because it is irreducible and we cannot get linear factors out of it, we're going to exclude option B. Constrain option C, our denominator contains x minus 3. It is a linear factor, but it is not repeated. Because it is not multiplied by itself. We're going to exclude option C. Option D contains X2 minus 4. This is a difference of squares which can be factored out as x minus 2. Multiplied by X + 2. So now we have two linear factors, X minus 2 and X + 2, but they are distinct, right? So these are distinct. And not repeated factors meaning d is also not the correct option. Therefore, the correct answer is a and a only. Thank you for watching.

2. Give an example of each of the following.
b. A repeated linear factor

Key Concepts

Polynomial Factors

Linear Factors

Repeated Factors

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