The cost of a chocolate is Rs. (x + y) and Amir bought (x + y) chocolates. Find the total amount paid by him in terms of x and y. If x =10, y =5 find the amount paid by him.

The length of a rectangle is (3x+2) units and it’s breadth is (3x–2) units. Find its area in terms of x. What will be the area if x = 20 units.

If two polynomials 2x³ + ax² + 4x – 12 and x³ + x² –2x+ a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.

If the polynomials f(x) = ax³ + 4x² + 3x –4 and g(x) = x³ – 4x + a leave the same remainder when divided by x–3, find the value of a. Also find the remainder.

Classify the following polynomials.

S.No	Polynomial	Based on number of terms	Based on their degree
1	\(\frac { { x }^{ 2 } }{ \sqrt { 2 } } +x+1\)
2	\(\sqrt { 5 } { x }^{ 2 }-\frac { 6 }{ 5 } x\)
3	1
4	\({ m }^{ 4 }-\frac { 6 }{ 7 } { m }^{ 2 }-6m+2.7\)
5	\(\frac { { t }^{ 3 } }{ \sqrt { 6 } } +\frac { { t }^{ 4 } }{ 4 } -t \)

Find the quotient and remainder when  5x³ - 9x² + 10x + 2 is divided by x + 2 using synthetic division

Find the quotient and remainder when 4x³ + 6x² + 7x + 2 is divided by x - 2

Find the quotient and remainder when 5x³ + 7x² + 3x + 2 is divided by 3x + 2

Factorise  2x³- x² - 12x - 9 into linear factors
 

Prove that x -1 is a factor x⁵ - 45x⁴ + 36x³ + 45x² - 36x^-1