Question

The remainder obtained when the polynomial $p\left(x\right)$ is divided by $(b-ax)$ is

• A. $p\left(-\frac{b}{a}\right)$
• B. $p\left(\frac{a}{b}\right)$
• C. $p\left(\frac{b}{a}\right)$
• D. $p\left(-\frac{a}{b}\right)$

Answer 1

The correct option is C

$p\left(\frac{b}{a}\right)$

Determine the remainder

If $f\left(x\right)$ is divided by $x+c$, then the remainder is $f\left(-c\right)$.$[\because x+c=x-(-c\left)\right]$

The divisor here is $x+c=b-ax$.

$\begin{array}{rcl}x+c& =& -\left(ax-b\right)\\ & =& -a\left(x-\left(\frac{b}{a}\right)\right)\left[\mathrm{Form}x-c\mathrm{with}c=\frac{b}{a}\right]\end{array}$

By remainder theorem, when $p\left(x\right)$ is divided by $b-ax$, then the remainder is $p\left(\frac{b}{a}\right)$.

Hence, the correct option is option $\left(\mathrm{C}\right)$.