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

Question

2. Give an example of each of the following.

d. A repeated irreducible quadratic factor

Accepted Answer

Welcome back, everyone. Which of the following is a repeated irreducible quadratic factor? Let's begin with A, we have 4 options to consider. A contains a factor Z2 + 2 Z + 5 squad. So first of all, is it repeated? The answer is yes because our factor is multiplied by itself due to the fact that it is squared, right? We can clearly show that this is a product between Z2 + 2 Z + 5 and Z2 + 2 Z + 5. It is repeated, right, because it is multiplied by itself at least once. In this case, it's multiplied by itself exactly once. The general condition is to have a factor that is multiplied by itself at least once. So yes, it is repeated. We can say R meaning repeated, and now is it irreducible. Let's recall that a quadratic factor is irreducible if it cannot be factored. Into linear factors and specifically the condition would be to have a discriminant less than 0. In this case, our discriminant is b2 minus 4 AC, so basically 22 minus 4 multiplied by 1, multiplied by 5, and this is 4 minus 20, which is -16. It is less than 0, meaning it is also irreducible I. So yes, it is repeated, yes, it is irreducible, meaning A is the correct option. Now, we can consider B. We already know that it is repeated because it's a square of Z2 minus 2 Z + 1. So, yes, it is repeated. Now, is it irreducible? We want to identify our discriminants that would be. B2, so negative 22 minus 4 AC, so we're subtracting 4 multiplied by 1 multiplied by 1. Our discriminant is 0. So this is greater than or equal to 0, meaning it is actually reducible, right? So, even though it's repeated, it's actually reducible, meaning B is not the correct option. Now considering options C. It is not repeated, right? So we can say not repeated and are because it's not repeated, we don't need to consider it because essentially we want to ensure that our Factor is irreducible and repeated. So in this case, because we don't have any exponent, it it says Z2 + 2 Z + 5, it is not repeated. Our factor is not multiplied by itself at least once. And now considering option D, we have two quadratic factors. One of them is. Z2 + 5. It is not repeated, right, because we don't have any exponent, and the other factor is Z2 + 2 Z + 5. Once again, it is not repeated because there is no exponent. Meaning we can exclude D. It is, it does not contain repeated quadratic factors. So C and D, those options do not have repeated quadratic factors. We did not need to check if they are reducible or not, because the first condition is not satisfied. Option B. Contains a repeated quadratic factor, but it is reducible and option A is the only correct option because we have a repeated irreducible quadratic factor. Thank you for watching.

2. Give an example of each of the following.d. A repeated irreducible quadratic factor

Watch next

2. Give an example of each of the following.
d. A repeated irreducible quadratic factor