csat-suneung 2020 Q14

csat-suneung · South-Korea · csat__math-humanities 4 marks Polynomial Division & Manipulation
Two polynomial functions $f ( x ) , g ( x )$ with integer constant terms and coefficients satisfy the following conditions. What is the maximum value of $f ( 2 )$? [4 points] (가) $\lim _ { x \rightarrow \infty } \frac { f ( x ) g ( x ) } { x ^ { 3 } } = 2$ (나) $\lim _ { x \rightarrow 0 } \frac { f ( x ) g ( x ) } { x ^ { 2 } } = - 4$
(1) 4
(2) 6
(3) 8
(4) 10
(5) 12
Two polynomial functions $f ( x ) , g ( x )$ with integer constant terms and coefficients satisfy the following conditions. What is the maximum value of $f ( 2 )$? [4 points]\\
(가) $\lim _ { x \rightarrow \infty } \frac { f ( x ) g ( x ) } { x ^ { 3 } } = 2$\\
(나) $\lim _ { x \rightarrow 0 } \frac { f ( x ) g ( x ) } { x ^ { 2 } } = - 4$\\
(1) 4\\
(2) 6\\
(3) 8\\
(4) 10\\
(5) 12