Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 303

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\[1)\ P(x) = 4x^{3} - x =\]

\[= x\left( 4x^{2} - 1 \right) =\]

\[= x(2x - 1)(2x + 1)\]

\[x = 2;\ \ x = \pm 0,5.\]

\[2)\ P(x) = x^{3} - x^{2} - 16x +\]

\[+ 16 = x^{2}(x - 1) -\]

\[- 16 \cdot (x - 1) =\]

\[= (x - 1)\left( x^{2} - 16 \right) =\]

\[= (x - 1)(x - 4)(x + 4)\]

\[x = \pm 4;\ \ x = 1.\]

\[3)\ P(x) = x^{3} + 2x^{2} - x - 2 =\]

\[= x\left( x^{2} - 1 \right) + 2 \cdot \left( x^{2} - 1 \right) =\]

\[= \left( x^{2} - 1 \right)(x + 2) =\]

\[= (x - 1)(x + 1)(x + 2)\]

\[x = - 2;\ \ x = \pm 1.\]

\[4)\ P(x) = 2x^{3} - x^{2} - 50x +\]

\[+ 25 = x^{2}(2x - 1) -\]

\[- 25 \cdot (2x - 1) =\]

\[= (2x - 1)\left( x^{2} - 25 \right) =\]

\[= (2x - 1)(x - 5)(x + 5)\]

\[x = \pm 5;\ \ x = 0,5.\]