A K Upadhyay and S Upadhyay Solutions for Chapter: Polynomials, Exercise 3: EXERCISE 2.3

Find the remainder when the polynomial $P\left(x\right)=x^4+2x^3-3x^2+x-1$ is divided by $(x-2)$.

Find the remainder when $f\left(x\right)=4x^3-12x^2+14x-3$ is divided by $x-\frac{1}{2}.$

Find the value of $k$ if the polynomial $P\left(x\right)=3x^3+k{x}^2+5x-16$ is divided by $(x-2)$ leaves a remainder $-8$.

If the polynomial $P\left(x\right)=x^4-2x^3+3x^2-ax+8$ is divided by $\left(x-2\right)$, it leaves a remainder $10.$ Find the value of $‘a’$.

If the polynomial $a{x}^3+4x^2+3x-4$ and $x^3-4x+a$ are divided by $(x-3)$ then the remainder in each case is same. Find the value of $a$

Let $R_1$ and $R_2$ are the remainder when the polynomial $4x^3+3x^2-12ax-5$ and $2x^3+a{x}^2-6x+2$ are divided by $(x-1)$ and $(x+2)$ respectively. if $3R_1+R_2=-28$, find the value of $\text{'}a\text{'}$

The polynomial $a{x}^3-3x^2+4$ and $2x^3-5x+a$ when divided by $(x-2)$ leaves the remainder $p$ and $q$ respectively. If $p-2q=4.$ Find the value of $a.$

The polynomial $a{x}^3+3x^2-3$ and $2x^3-5x+a$ when divided by $(x-4)$ leave the same remainder in each case. Find the value of $a.$