Tamil Nadu Board Solutions for Chapter: Algebra, Exercise 12: Exercise

The area of a rectangle is $x^2+7x+12.$ If its breadth is $(x+3)$, then find its length.

The base of a parallelogram is $(5 x+4)$. Find its height, if the area is $25x^2-16$

Find the quotient and remainder for the following using synthetic division: 

$\left(x^3+2x^2-x-4\right)÷(x+2)$

Find the quotient and remainder for the following using synthetic division: 

$\left(3x^3-2x^2+7x-5\right)÷(x+3)$

Find the quotient and remainder for the following using synthetic division: 

$\left(8x^4-2x^2+6x+5\right)÷(4x+1)$

 If the quotient obtained on dividing  $\left(8x^4-2x^2+6x-7\right)$ by $(2x+1)$ is $\left(4x^3+p{x}^2-qx+3\right)$ then find $\mathrm{p},\mathrm{q}$ and also the remainder.

If the quotient obtained on dividing $3x^3+11x^2+34x+106$ by $x-3$ is $3x^2+ax+b$ then find $a,b$ and also the remainder.

If $f\left(x\right)=x^2-4x+3$, then find the values of $f\left(1\right), f\left(-1\right), f\left(2\right), f\left(3\right)$. Also find the zeros of the polynomial $f\left(x\right)$.