Question

There are x⁴+57x+15 pens to be distributed in a class of x²+4x+2 students. Each student should get the maximum possible number of pens. Find the number of pens received by each student and the number of pens left undistributed (x ∈ N).

Answer 1

number of pens to be distributed in a class = x⁴ + 57x + 15
number of students in class = x² + 4x + 2

here, dividend polynomial , P(x) = x⁴ + 57x + 15
divisor polynomial , g(x) = x² + 4x + 2,

x² + 4x + 2)x⁴ + 57x + 15 ( x² - 4x + 14
x⁴ + 4x³ + 2x²
----------------------
-4x³ - 2x² + 57x
- 4x³ - 16x² - 8x
--------------------------
+ 14x² + 65x + 15
+ 14x² + 56x + 28
-----------------------------
9x - 13

hence , quotient polynomial, q(x) = x² - 4x + 14
and the remainder polynomial , r(x) = 9x - 13
therefore, each student will get (x² - 14x + 14) pens and number of pens left undistributed = (9x - 13)

Answer 2

Answer:

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