因数 8c^6+19c^3-27

解

因数

8 c^{6} + 19 c^{3} - 27

(c - 1) (c^{2} + c + 1) (2 c + 3) (4 c^{2} - 6 c + 9)

解答ステップ

8 c^{6} + 19 c^{3} - 27

有理根定理を使用する

= (c - 1) \frac{8 c ^{6} + 19 c ^{3} - 27}{c - 1}

\frac{8 c ^{6} + 19 c ^{3} - 27}{c - 1} = 8 c^{5} + 8 c^{4} + 8 c^{3} + 27 c^{2} + 27 c + 27

= (c - 1) (8 c^{5} + 8 c^{4} + 8 c^{3} + 27 c^{2} + 27 c + 27)

因数

8 c^{5} + 8 c^{4} + 8 c^{3} + 27 c^{2} + 27 c + 27 : (c^{2} + c + 1) (2 c + 3) (2^{2} c^{2} - 3 \cdot 2 c + 3^{2})

= (c - 1) (c^{2} + c + 1) (2 c + 3) (2^{2} c^{2} - 3 \cdot 2 c + 3^{2})

簡素化

(c - 1) (c^{2} + c + 1) (2 c + 3) (2^{2} c^{2} - 3 \cdot 2 c + 3^{2}) : (c - 1) (c^{2} + c + 1) (2 c + 3) (4 c^{2} - 6 c + 9)

= (c - 1) (c^{2} + c + 1) (2 c + 3) (4 c^{2} - 6 c + 9)