is (x-3) a factor of x^3 -14x^2 + 41x +56
To determine if (x - 3) is a factor of x^3 - 14x^2 + 41x + 56, we need to perform polynomial long division or synthetic division to see if the remainder is equal to 0.
Performing polynomial division:
x^2 - 11x - 4
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x - 3 | x^3 - 14x^2 + 41x + 56
- (x^3 - 3x^2)
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- 11x^2 + 41x
- (- 11x^2 + 33x)
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8x + 56
- (8x - 24)
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80
The remainder is 80, which means (x - 3) is not a factor of x^3 - 14x^2 + 41x + 56.