Question:
if the polynomial x4-2x3-8x2 mx-5 is exactly divisible by x 3 then find m.
Answer:
Given, x4 - 2x3 - 8x2 + mx - 5 is exactly divisible by x + 3
So, x + 3 is a root of the given polynomial.
Now, put x + 3 = 0
=> x = -3 in the given polynomial, we get
(-3)4 - 2(-3)3 - 8(-3)2 + m*(-3) - 5 = 0
=> 81 + 2*27 - 8*9 - 3m - 5 = 0
=> 81 + 54 - 72 - 3m - 5 = 0
=> 135 - 77 - 3m = 0
=> 58 - 3m = 0
=> 3m = 58
=> m = 58/3
So, the value of m is 58/3
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