tmua None Q12

tmua · Uk · specimen_paper2 Factor & Remainder Theorem Remainder by Linear Divisor
12. A polynomial $p ( x )$ has the property that $p ( 1 ) = 2$.
Which one of the following can be deduced from this?
A $\quad p ( x ) = ( x - 1 ) q ( x ) + 2$ for some polynomial $q ( x )$.
B $\quad p ( x ) = ( x + 1 ) q ( x ) + 2$ for some polynomial $q ( x )$.
C $\quad p ( x ) = ( x - 1 ) q ( x ) - 2$ for some polynomial $q ( x )$.
D $\quad p ( x ) = ( x + 1 ) q ( x ) - 2$ for some polynomial $q ( x )$.
E $\quad p ( x ) = ( x - 2 ) q ( x ) + 1$ for some polynomial $q ( x )$. F $\quad p ( x ) = ( x + 2 ) q ( x ) + 1$ for some polynomial $q ( x )$. G $\quad p ( x ) = ( x - 2 ) q ( x ) - 1$ for some polynomial $q ( x )$. H $\quad p ( x ) = ( x + 2 ) q ( x ) - 1$ for some polynomial $q ( x )$.
12. A polynomial $p ( x )$ has the property that $p ( 1 ) = 2$.

Which one of the following can be deduced from this?

A $\quad p ( x ) = ( x - 1 ) q ( x ) + 2$ for some polynomial $q ( x )$.\\
B $\quad p ( x ) = ( x + 1 ) q ( x ) + 2$ for some polynomial $q ( x )$.\\
C $\quad p ( x ) = ( x - 1 ) q ( x ) - 2$ for some polynomial $q ( x )$.\\
D $\quad p ( x ) = ( x + 1 ) q ( x ) - 2$ for some polynomial $q ( x )$.\\
E $\quad p ( x ) = ( x - 2 ) q ( x ) + 1$ for some polynomial $q ( x )$.\\
F $\quad p ( x ) = ( x + 2 ) q ( x ) + 1$ for some polynomial $q ( x )$.\\
G $\quad p ( x ) = ( x - 2 ) q ( x ) - 1$ for some polynomial $q ( x )$.\\
H $\quad p ( x ) = ( x + 2 ) q ( x ) - 1$ for some polynomial $q ( x )$.\\