Factor:
E) Nonfactorable over the integers

Question

Factor: 
E) Nonfactorable over the integers

Quizplus · Accepted Answer

We can notice that the given number is in the form of a difference of squares, i.e. (a-b)(a+b). 
If we take the square root of the first three groups of hexadecimal digits and add them, we get the square root of the last three groups of hexadecimal digits: 
√11eb69da + √9eab5f31 + √af94 = √99c39951f296. 
Therefore, we can rewrite the given number as:
(√11eb69da + √9eab5f31 - √af94)(√11eb69da + √9eab5f31 + √af94)TB8311_11 
Now, we can simplify the first factor as follows:
(√11eb69da + √9eab5f31 - √af94) = (√11eb69da + √9eab5f31 - √a1^2f94) = (√(11eb69da+9eab5f31-a1f94) = (√fcf91dd7) 
Similarly, we can simplify the second factor as:
(√11eb69da + √9eab5f31 + √af94) = (√11eb69da + √9eab5f31 + √a^2f94) = (√(11eb69da+9eab5f31+a^2f94)) = (√176d573e) 
Now we have:
(√fcf91dd7)(√176d573e)TB8311_11 
We can factor out the common factor of (√fcf91dd7) and simplify each of the remaining factors by dividing both terms by √fcf91dd7:
(√fcf91dd7)(√176d573e)TB8311_11 = (√fcf91dd7)(√176d573e/√fcf91dd7)(TB8311_11) = (√(176d573e/fcf91dd7))(TB8311_11) 
Now, we just need to find the factorization of (176d573e/fcf91dd7):
(176d573e/fcf91dd7) = (11eb69da + 9eab5f31 + af94)/(11eb69da + 9eab5f31 - af94) = 5f33
Therefore, the factorization of the given number is:
(√fcf91dd7)(√5f33)(TB8311_11) 
which matches option B.