cmi-entrance 2014 QA8

cmi-entrance · India · ugmath 4 marks Factor & Remainder Theorem Remainder by Quadratic or Higher Divisor

Let $f ( x ) = 7 x ^ { 32 } + 5 x ^ { 22 } + 3 x ^ { 12 } + x ^ { 2 }$. (i) Find the remainder when $f ( x )$ is divided by $x ^ { 2 } + 1$. (ii) Find the remainder when $x f ( x )$ is divided by $x ^ { 2 } + 1$. In each case your answer should be a polynomial of the form $a x + b$, where $a$ and $b$ are constants.

Let $f ( x ) = 7 x ^ { 32 } + 5 x ^ { 22 } + 3 x ^ { 12 } + x ^ { 2 }$. (i) Find the remainder when $f ( x )$ is divided by $x ^ { 2 } + 1$. (ii) Find the remainder when $x f ( x )$ is divided by $x ^ { 2 } + 1$. In each case your answer should be a polynomial of the form $a x + b$, where $a$ and $b$ are constants.

Paper Questions

QA1 QA10 QA11 QA12 QA2 QA3 QA4 QA5 QA6 QA7 QA8 QA9 QB1 QB2 QB3 QB4 QB5 QB6