R S Aggarwal and Veena Aggarwal Solutions for Exercise 3: EXERCISE 2C

Using the remainder theorem, find the remainder when $p\left(x\right)$ is divided by $g\left(x\right)$, where $p\left(x\right)=2x^3-9x^2+x+15, g\left(x\right)=2x-3$.

Using the remainder theorem, find the remainder, when $p\left(x\right)$ is divided by $g\left(x\right)$ where 

 $p\left(x\right)=x^3-2x^2-8x-1, g\left(x\right)=x+1$

Using the remainder theorem, find the remainder, when $p\left(x\right)$ is divided by $g\left(x\right)$ where $p\left(x\right)=2x^3+x^2-15x-12, g\left(x\right)=x+2$.

Find the remainder when $p\left(x\right)$ is divided by $g\left(x\right)$, where $p\left(x\right)=6x^3+13x^2+3, g\left(x\right)=3x+2$.

Find the remainder when $p\left(x\right)$ is divided by $g\left(x\right)$, where $p\left(x\right)=2x^3-9x^2+x+15 \& g\left(x\right)=2x-3$.

Using the remainder theorem, find the remainder, when $p\left(x\right)$ is divided by $g\left(x\right)$ where $p\left(x\right)=2x^3+3x^2-11x-3, g\left(x\right)=\left(x+\frac{1}{2}\right)$

If $p\left(x\right)=x^3-5x^2+4x-3$ and $g\left(x\right)=x-2$, show that $p\left(x\right)$ is not a multiple of $g\left(x\right)$.

If $p\left(x\right)=2x^3-11x^2-4x+5$ and $g\left(x\right)=2x+1$, show that $g\left(x\right)$ is not a factor of $p\left(x\right)$.