Odpowiedź:
h = -10x^6 - 24x^5 + 8x^4 + 24x - 7
h (-1) = -9
Szczegółowe wyjaśnienie:
h = 3f(x) - 4g(x)
f(x) = -2x^6 + 4x^3 -8x^5 + 5
g(x) = x^6 - 2x^4 + 3x^3 -6x+2
3f(x) = 3 razy (-2x^6 + 4x^3 -8x^5 + 5) = -6x^6 + 12x^3 - 24x^5 + 15
4g(x) = 4 razy (x^6 - 2x^4 + 3x^3 -6x+2) = 4x^6 - 8x^4 + 12x^3 - 24x + 8
h = 3f(x) - 4g(x) = -6x^6 + 12x^3 - 24x^5 + 15 - (4x^6 - 8x^4 + 12x^3 - 24x + 8)
= -6x^6 + 12x^3 - 24x^5 + 15 - 4x^6 + 8x^4 - 12x^3 + 24x - 8 =
= -10x^6 - 24x^5 + 8x^4 + 24x - 7
dla h = -1 mamy:
-10x^6 - 24x^5 + 8x^4 + 24x - 7 = (-10 razy (-1)^6) - (24 razy (-1)^5) + (8 razy (-1)^4) + (24 razy (-1)) - 7 = -10 + 24 + 8 -24 - 7 = -9