Вправа 642 алгебра Бевз гдз 7 клас

№ 642

а) 3х⁵ – х⁴ – 3х + 1 = x⁴(3x – 1) – (3x – 1) = (3x – 1)(x⁴ – 1) =
= (3x – 1)(x² – 1)(x² + 1) = (3x + 1)(x² + 1)(x – 1)(x + 1);
б) 2а² + а³ – 18а⁴ – 9а⁵ = a²(2 + a) – 9a⁴(2 + a) =
= (2 + a)(a² – 9a4) = (2 + a)(a – 3a²)(a + 3a²) =
= (2 + a)(1 – 3a)(1 + 3a) • a²;
в) х⁴ – 37х² + 36 = x⁴ – 36x² – x² + 36 =
= (x² – 6x)(x² + 6x) – (x – 6)(x + 6) =
= x²(x – 6)(x + 6) – (x – 6)(x + 6) = (x – 6)(x + 6)(x² – 1) =
= (x – 6)(x + 6)(x – 1)(x + 1).