Question

2 Найдите значение многочлена Р(х) в точке x = а.
1) Р(х) = x3 +4х2 + 3x +11, а = – 3;
2) Р(х) = 3х6 — х3 – 12х2 – 51, а = — 2;
3) Р(х) = 3х4 — х2 + x — 31, а = 2;
4) Р(х) = — 3х5 +2х3 – 4х2 – 2х + 10, а=-1​

Answer 1

Ответ:

1) Р(х) = x³ +4·x² + 3·x +11, а = –3

Р(–3) = (–3)³ +4·(–3)² + 3·(–3) +11= –27+4·9–9 = –36+36 = 0

2) Р(х) = 3·x⁶ – x³ – 12·x² – 51, а = –2

Р(–2) = 3·(–2)⁶ – (–2)³ – 12·(–2)² – 51 = 3·64 + 8 – 12·4 – 51=

= 192 + 8 – 48 – 51 = 200 – 99 = 101

3) Р(х) = 3·x⁴ – x² + x – 31, а = 2

Р(2) = 3·2⁴ – 2² + 2 – 31 = 3·16 – 4 + 2 – 31 = 48 – 33 = 15

4) Р(х) = – 3·x⁵ +2·x³ – 4·x² – 2·x + 10, а= –1​

Р(–1) = – 3·(–1)⁵ +2·(–1)³ – 4·(–1)² – 2·(–1) + 10 =

= – 3·(– 1) + 2·(– 1) – 4·1 + 2 + 10 = 3 – 2 – 4 + 12 = 9