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Determine k so that (x-2) is a factor of (x^4 - 2x^3 + kx + 6)

User Aniket Rao
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1 Answer

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19 votes

To determine k so that (x-2) is a factor of (x^4 - 2x^3 + kx + 6), we could use the fact that:

If x-2 is a factor, then x=2 is a zero.

Now, we know that a polynomial has a zero when it becomes zero, so, if we replace x=2 in the expression and the result is zero, that means that x=2 is actually a zero:

Therefore, k = -3 so that (x-2) is a factor of x^4 - 2x^3 + kx + 6

Determine k so that (x-2) is a factor of (x^4 - 2x^3 + kx + 6)-example-1
User Raymond Feng
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3.0k points