Question

Разложите на множители:1)x^3+6x^2+11x+6;2)x^4+x^3+6x^2+5x+5​

Answer 1

$x {}^{3} + 6x {}^{2} + 11x + 6 \\ x {}^{3} + x{}^{2} + 5x {}^{2} + 5x + 6x + 6 \\ x {}^{2} (x + 1) + 5x \times (x + 1) + 6(x + 1) \\ (x + 1) \times (x {}^{2} + 5x + 6) \\ (x + 1) \times (x \times (x + 3) + 2(x + 3)) \\ (x + 1) \times (x + 3) \times (x + 2) \\ \\ 2) x {}^{4} + x {}^{3} + 6x {}^{2} + 5x + 5 \\ x {}^{4} + x {}^{3} + x {}^{2} + 5x {}^{2} + 5x + 5 \\ x {}^{2}(x {}^{2} + x + 1) + 5(x {}^{2} + x + 1) \\ (x {}^{2} + x + 1) \times (x {}^{2} + 5)$

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