Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.

Question

Using the factors  and  , find the remaining factor(s) of  and write the polynomial in fully factored form.

Quizplus · Accepted Answer

We can use the difference of squares to factor the given factors:

11eb11e8_19c7_799a_ad38_3d93ad8c683b_TB4588_11 = (11eb11e8_19c7_799c_ad38_87cd5fed9437_TB4588_11 - 11038b_16)(11eb11e8_19c7_799c_ad38_87cd5fed9437_TB4588_11 +11038b_16)
11eb11e8_19c7_799b_ad38_dba8637898bf_TB4588_11 = (11eb11e8_19c7_799c_ad38_87cd5fed9437_TB4588_11 - 11038c_16)(11eb11e8_19c7_799c_ad38_87cd5fed9437_TB4588_11 + 11038c_16)

Now, we can see that the remaining factors must be of the form (11eb11e8_19c7_799c_ad38_xxxxxxxx_TB4588_11 - 11038b_16)(11eb11e8_19c7_799c_ad38_xxxxxxxx_TB4588_11 + 11038b_16), where xxxxxxxx is some hex value. 
Comparing the third hex digits of the given factors, we see that they differ by 1 (9a and 9b). This means that the third hex digit of the remaining factor(s) must be a, as adding or subtracting 1 from a would give us either 9b or 9a. 
Looking at the answer choices, we can see that only option B has a third hex digit of a, so it must be the correct choice. 
Thus, the fully factored form of the polynomial is:
11eb11e8_19c7_799c_ad38_87cd5fed9437_TB4588_11 = (11eb11e8_19c7_799c_ad38_a0ae436a01a6bc8f_TB4588_11 - 11038b_16)(11eb11e8_19c7_799c_ad38_a0ae436a01a6bc8f_TB4588_11 + 11038b_16)

Using the Factors and , Find the Remaining