In a given set of numbers, identify which are integers, rational, irrational, and imaginary. and Explain your answer,
-5 12; 6; −157; −8−−−√3; 2–√; −4−−−√; 3 + 5i; 23; 0; 1.6333...; π; 8–√; -5;

Please if someone can help me with this,

The distance from his home to the store is represented by

41x² + 357x - 15.

We know the distance from the store to the library, and the distance from his home to the library.  We also know the store is between the two.  To find the missing distance, we subtract the two polynomials we have:

(54x² + 310x + 8) - (13x² - 47x + 23)

Combining like terms:
54x² - 13x² = 41x²;
310x -- 47x = 310x + 47x = 357x;
8-23 = -15

This gives us 

41x²+357x-15