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ГДЗ Алгебра 7 клас Тарасенкова (2024)
Роздiл 3. Одночлени i многочлени
Реклама:
Розкладіть на множники многочлен:
1) x2 – 5x + 6 = (x2 – 4x + 4) – x + 2 = (x – 2)2 – (x – 2) – (x – 2)(x – 2 – 1) = (x – 2)(x –3). 2) y2 – 3y + 2 = (y2 – 2y + 2) – у + 1 = (у – 1)2 = (у – 1) = (у – 1) • (y – 1 – 1) = (у – 1)(y – 2).
3) x4 + 5x2 – 6 = (x2)2 + 2 • x2 • 2,5 + 2,52 – 2,52 – 6 = (x2 + 2,5)2 – 6,25 – 6 = (х2 + 2,5)2 – 12,25 = (х2 + 2 ,5)2 – 3,52 = (х2 + 2,5 – 3,5)(x2 + 2,5 + 3,5) = (х2 + 6)(x2 – 1) = (х2 + 6)(х – 1)(x + 1);
4) x4 – Зх2 – 4 = (x2)2 – 2 • x2 • 1,5 + 1,52 – 1,52 – 4 = (х2 – 1,5)2 – – 6,25 = (х2 – 1,5)2 – 2,52 = (х2 –1,5 – 2,5)(x2 – 1,5 + 2,5) = (х2 –4) • (х2 + 1) = (х – 2)(х + 2)(х2 + 1).
1) x2 – 5x + 6 = (x2 – 4x + 4) – x + 2 = (x – 2)2 – (x – 2) – (x – 2)(x – 2 – 1) = (x – 2)(x –3). 2) y2 – 3y + 2 = (y2 – 2y + 2) – у + 1 = (у – 1)2 = (у – 1) = (у – 1) • (y – 1 – 1) = (у – 1)(y – 2).
3) x4 + 5x2 – 6 = (x2)2 + 2 • x2 • 2,5 + 2,52 – 2,52 – 6 = (x2 + 2,5)2 – 6,25 – 6 = (х2 + 2,5)2 – 12,25 = (х2 + 2 ,5)2 – 3,52 = (х2 + 2,5 – 3,5)(x2 + 2,5 + 3,5) = (х2 + 6)(x2 – 1) = (х2 + 6)(х – 1)(x + 1);
4) x4 – Зх2 – 4 = (x2)2 – 2 • x2 • 1,5 + 1,52 – 1,52 – 4 = (х2 – 1,5)2 – – 6,25 = (х2 – 1,5)2 – 2,52 = (х2 –1,5 – 2,5)(x2 – 1,5 + 2,5) = (х2 –4) • (х2 + 1) = (х – 2)(х + 2)(х2 + 1).