Find the value of a if (x-a) is a factor of the polynomial.

x⁶- ax⁵+ x⁴- ax³+ 3x- a+ 2

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Solution

If x - a satisfies the given equation then that means that x = a is a root of the equation. This means that substituting a instead of x in the given equation should give 0.

Thus a^6 - a^6 + a^4 - a^4 +3a - a +2 = 0

or that 2a = -2

or that the value of a is -1.

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