Question

(FCC-BA/Modificada) Dado o polinômio P(x) =
x³ − 2x² − mx −1, onde m ε R. Se P(2) = 3P(1), então o valor P(3) é:
A) 1
B) 9
C) 13
D) 19
E) 23

Answer 1

$\sf P(x) = x^3-2x^2-mx-1 \\\\ P(2) = 3P(1) \\\\ 2^3-2\cdot 2^2-m\cdot 2-1 = 3\cdot (1^3-2\cdot 1^2-m\cdot 1 - 1 ) \\\\\ 8-8-2\cdot m-1 = 3\cdot (1-2-m-1) \\\\\ -2\cdot m - 1 = 3\cdot (-2-m) \\\\ -2\cdot m -1= -6 - 3\cdot m \\\\ 3\cdot m - 2\cdot m = -6+1 \\\\ \boxed{\sf m = -5 }\\\\\ Portanto : \\\\ P(x) = x^3-2\cdot x^2+5\cdot x-1 \\\\ \text{Fa{\c c}amos P(3) }: \\\\ P(3) = 3^3-2\cdot 3^2+5\cdot 3 - 1 \\\\ P(3) = 27-18+15-1 \\\\ P(3) = 9+14 \\\\ \huge\boxed{\sf P(3) = 23 } \checkmark$

letra E