9.4 a) 7c^2 - c - c^3 + 7; в) x^3 - 6 + 2x - 3x^2; б) x^3 + 28 - 14x^2 - 2x; г) 2b^3 - 6 - 4b^2 + 3b

Привет! Давай разложим эти многочлены на множители методом группировки. ### Задание 9.4 а) $7c^2 - c - c^3 + 7 = (7c^2 + 7) - (c^3 + c) = 7(c^2 + 1) - c(c^2 + 1) = (c^2 + 1)(7 - c)$ б) $x^3 + 28 - 14x^2 - 2x = (x^3 - 14x^2) - (2x - 28) = x^2(x - 14) - 2(x - 14) = (x - 14)(x^2 - 2)$ в) $x^3 - 6 + 2x - 3x^2 = (x^3 - 3x^2) + (2x - 6) = x^2(x - 3) + 2(x - 3) = (x - 3)(x^2 + 2)$ г) $2b^3 - 6 - 4b^2 + 3b = (2b^3 - 4b^2) + (3b - 6) = 2b^2(b - 2) + 3(b - 2) = (b - 2)(2b^2 + 3)$ ### Задание 9.5 а) $16ab^2 + 5b^2c + 10c^3 + 32ac^2 = (16ab^2 + 32ac^2) + (5b^2c + 10c^3) = 16a(b^2 + 2c^2) + 5c(b^2 + 2c^2) = (b^2 + 2c^2)(16a + 5c)$ б) $20n^2 - 35a - 14an + 50n = (20n^2 + 50n) - (14an + 35a) = 10n(2n + 5) - 7a(2n + 5) = (2n + 5)(10n - 7a)$ в) $18a^2 + 27ab + 14ac + 21bc = (18a^2 + 27ab) + (14ac + 21bc) = 9a(2a + 3b) + 7c(2a + 3b) = (2a + 3b)(9a + 7c)$ г) $2x^2yz - 15yz - 3xz^2 + 10xy^2 = (2x^2yz + 10xy^2) - (3xz^2 + 15yz) = 2xy(xz + 5y) - 3z(xz + 5y) = (xz + 5y)(2xy - 3z)$ ### Задание 9.6 а) $40a^3bc + 21bc - 56ac^2 - 15a^2b^2 = (40a^3bc - 15a^2b^2) - (56ac^2 - 21bc) = 5a^2b(8ac - 3b) - 7c(8ac - 3b) = (8ac - 3b)(5a^2b - 7c)$ б) $16xy^2 - 5y^2z - 10z^3 + 32xz^3 = (16xy^2 + 32xz^3) - (5y^2z + 10z^3) = 16x(y^2 + 2z^3) - 5z(y^2 + 2z^3) = (y^2 + 2z^3)(16x - 5z)$ в) $30x^2 + 10c - 25cx - 12x = (30x^2 - 12x) - (25cx - 10c) = 6x(5x - 2) - 5c(5x - 2) = (5x - 2)(6x - 5c)$ г) $18x^2z - 10kxy + 20k^2y - 36kxz = (18x^2z - 36kxz) - (10kxy - 20k^2y) = 18xz(x - 2k) - 10ky(x - 2k) = (x - 2k)(18xz - 10ky) = 2(x - 2k)(9xz - 5ky)$