When the polynomial f(x) is divided by x3 - 2, the quotient and remainder are x2 + 4x - 1 and x, respectively. Determine the value f(3).
+26379 When the polynomial f(x) is divided by x3 - 2, the quotient and remainder are x2 + 4x - 1 and x, respectively. Determine the value f(3).
\(\begin{array}{rcll} \dfrac{f(x)}{x^3-2} &=& x^2+4x-1+\dfrac{x}{x^3-2} \qquad | \qquad \cdot (x^3-2) \\ f(x) &=& (x^2+4x-1) \cdot (x^3-2)+ x \\ f(3) &=& (3\cdot 3+4\cdot 3-1)\cdot(3\cdot 3 \cdot 3 - 2) + 3 \\ f(3) &=& (9+12-1)\cdot (27-2) +3 \\ f(3) &=& 20\cdot 25 +3 \\ f(3) &=& 500 +3 \\ \mathbf{f(3)} &\mathbf{=}& \mathbf{503} \end{array}\)
