Вправа 643 алгебра Бевз гдз 7 клас

№ 643

а) с⁵ – 16с – с⁴ + 16 = c(c⁴ – 16) – (c⁴ – 16) = (c⁴ – 16)(c – 1) =
= (c² + 4)(c² – 4)(c – 1) = (c² + 4)(c – 1)(c – 2)(c + 2);
б) 2х² – х³ – 2х⁴ + х⁵ = x²(2 – x) – x⁴(2 – x) = (2 – x)(x² – x4) =
= (2 – x)(x – x²)(x + x²) = (2 – x)(1 – x)(1 + x)x²;
в) х⁴ – 26х² + 25 = x⁴ – 25x² + 25 – x² = (x² – 5)² – x² =
= (x² – 5 + x²)(x² – 5 – x²) = (2x² – 5) • (–5) = –5 • (2x² – 5).