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check whether the polynomial p(x)=4x³+4x²-x-1 is a multiple of 2x+1

$Let {p(x)=4x}^{3} + 4 x^{2} - x - 1 q (x) = 2 x + 1 \Rightarrow q (x) = 0 \Rightarrow 2 x + 1 = 0 \Rightarrow x = \frac{- 1}{2} If the given polynomial must be the multiple of 2x+1 the n p (\frac{- 1}{2}) = 0 \Rightarrow 4 (\frac{- 1}{2})^{3} + 4 (\frac{- 1}{2})^{2} - (\frac{- 1}{2}) - 1 = 4 (\frac{- 1}{8}) + 4 (\frac{1}{4}) + \frac{1}{2} - 1 = \frac{- 1}{2} + 1 + \frac{1}{2} - 1 = 0 So the given polynomial is a multiple of 2x+1$

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