Answer:
To find the value of c such that the polynomial p(x) = -x^3 + cx^2 - 4x + 3 is divisible by (x - 3), we need to perform polynomial division and check for the remainder.
Performing polynomial division, we divide p(x) by (x - 3):
-x^2 - 2cx - 6
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x - 3 | -x^3 + cx^2 - 4x + 3
-(-x^3 + 3x^2)
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-2x^2 - 4x
-(-2x^2 + 6x)
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-10x + 3
-(-10x + 30)
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-27
The remainder of the division is -27. For p(x) to be divisible by (x - 3), the remainder should be zero. Therefore, we need to find the value of c such that the remainder is zero, i.e., -27 = 0.
Since -27 is not equal to zero, there is no value of c that makes p(x) divisible by (x - 3).