Embibe Experts Solutions for Chapter: Algebra, Exercise 1: Tamilnadu Board-2018

What can be a degree of the remainder atmost, when a fourth-degree polynomial is divided by a quadratic polynomial?

The LCM of $x^3 – a^3$ and ${(x – a)}^2$ is:

If $A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha \end{array}\right]$ is such that $A^2=I$, then:

A matrix consists of $30$ elements. What are the possible orders it can have?

If $A=\left(\begin{array}{cc}3& 2\\ 4& 0\end{array}\right)$ and $B=\left(\begin{array}{cc}3& 0\\ 3& 2\end{array}\right)$, then find $AB$ and $BA$.

Solve the equation $x^2-\left(\sqrt{3}+1\right)x+\sqrt{3}=0$ by completing the square method

Draw the graph of $y=x^2+3x+2$ and use it to solve the equation $x^2+2x+4=0$.

If the remainder on division $x^3+2x^2+kx+3$ by $x-3$ is $21$, find the value of $k$ and hence find the zeroes of the cubic polynomial $x^3+2x^2+kx-18$.