R S Aggarwal and Veena Aggarwal Solutions for Exercise 2: Exercise 2B

Find the quotient and the remainder when
$f\left(x\right)=$$x^3-3x^2+5x-3$ is divided by $g\left(x\right)=$$x^2-2$.

On dividing $3x^3+x^2+2x+5$ by a polynomial $g\left(x\right)$, the quotient and remainder are $(3x – 5)$ and $(9x + 10)$respectively. Find $g\left(x\right)$.

Verify division algorithm for the polynomial $f\left(x\right)=(8+20x+x^2–6x^3)$ and $g\left(x\right)=(2+5x–3x^2)$.

It is given that $–1$ is one of the zeros of the polynomial $x^3+2x^2–11x–12$. Find all the zeros of the given polynomial.

If$1$ and$–2$ are two zeroes of the polynomial $(x^3–4x^2–7x+10)$, find its third zero.

If$3$ and $–3$are two zeroes of the polynomial $(x^4+x^3–11x^2–9x+18)$, find all the zeroes of the given polynomial.

Find all the zeroes of $(x^4+x^3–23x^2–3x+60)$, if it is given that two of its zeroes are $\sqrt{3}$ and $-\sqrt{3}$.

Obtain all other zeros of $(x^4+4x^3–2x^2–20x–15)$  if two of its zeros are $\sqrt{5}$ and $-\sqrt{5}$.