Solve: $P (- 2) = (- 2)^{3} + 2 (- 2)^{2} + (- 2)^{4}$

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Solution

$P (- 2) = {(- 2)}^{3} + 2 {(- 2)}^{2} + {(- 2)}^{4} = {(- 2)}^{3} + 2^{1} \times {(- 2)}^{2} + {(- 2)}^{4} = {(- 2)}^{3} - (2^{1} \times 2^{2}) + {(- 2)}^{4} = {(- 2)}^{3} - 2^{1 + 2} + {(- 2)}^{4} = {(- 2)}^{3} - 2^{3} + {(- 2)}^{4} = - 8 - 8 + 16 = - 16 + 16 = 0.$

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