Question

If a polynomial gives remainder $1$ and $2$ and same quotient on dividing by $x-2$ and $x-1$ respectively, then the remainder when that polynomial is divided by $x^2-3x+2,$ is

• A. $x-3$
• B. $-x+3$
• C. $x-2$
• D. $-x+2$

Answer 1

The correct option is B $-x+3$

when $p\left(x\right)$ is divided by $x^2-3x+2$ then remainder should be of the form $ax+b$ as degree of remainder should be less than the divisor

according to the given in the question, $p\left(1\right)=2$ and $p\left(2\right)=1$

$p\left(x\right)=(x^2-3x+2)h\left(x\right)+ax+b$

$p\left(1\right)=a+b=2$ and $p\left(2\right)=2a+b=1$

using these two equations,$a=-1$ & $b=3$

hence remainder$=-x+3$