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Problem 9

What is the value of c if x⁶+cx⁴+32 is divisble by x-2?

Solution

Since x⁶+cx⁴+32 is divisble by x-2 then we know that 2 must make this polynomial zero.
Plugging 2 in we get (2)⁶+c(2)⁴+32=0
=>64+16c+32=0
=>16c=-96
=>c=-6
Thus c=-6.