Question

Find the constant c such that the denominator will divide evenly into the numerator

x^5-2X^2+x+c/ X+2

Answer 1

If f ( x ) = x^5 - 2 x^2 + x + c is divisible by : x + 2
then : f ( - 2 ) = 0
f ( - 2 ) = ( - 2 )^5 - 2 ( - 2 ) ^2 + ( - 2 ) + c = 0
- 32 - 8 - 2 + c = 0
c = 32 + 8 + 2
Answer:
c = 42

Answer 2

Let f(x) = x^5 - 2x^2 + x + c
For the denominator to divide numerator, then
f(-2) = 0
(-2)^5 - 2(-2)^2 - 2 + c = 0
-32 - 2(4) - 2 + c = 0
-32 - 8 - 2 + c = 0
-42 + c = 0
c = 42.

The constant c = 42.