**Chapter 3 Polynomials Practice Set 3.2**

Chapter 3 Polynomials Practice Set 3.2

**Question 1.Use the given letters to write the answer.i. There are â€˜aâ€™ trees in the village Lat. If the number of trees increases every year by â€™bâ€˜. then how many trees will there be after â€˜xâ€™ years?ii. For the parade there are y students in each row and x such row are formed. Then, how many students are there for the parade in all ?iii. The tens and units place of a two digit number is m and n respectively. Write the polynomial which represents the two digit number.Solution:**

i. Number of trees in the village Lat = a

Number of trees increasing each year = b

âˆ´ Number of trees after x years = a + bx

âˆ´ There will be a + bx trees in the village Lat after x years.

ii. Total rows = x

Number of students in each row = y

âˆ´ Total students = Total rows Ã— Number of students in each row

= x Ã— y

= xy

âˆ´ There are in all xy students for the parade.

iii. Digit in units place = n

Digit in tens place = m

âˆ´ The two digit number = 10 x digit in tens place + digit in units place

= 10m + n

âˆ´ The polynomial representing the two digit number is 10m + n.

**Question 2.Add the given polynomials.i. x**

^{3}â€“ 2x

^{2}â€“ 9; 5x

^{3}+ 2x + 9ii. -7m

^{4}+ 5m

^{3}+ âˆš2 ; 5m

^{4}â€“ 3m

^{3}+ 2m

^{2}+ 3m â€“ 6iii. 2y

^{2}+ 7y + 5; 3y + 9; 3y

^{2}â€“ 4y â€“ 3Solution:

= 5y

^{2}+ 6y + 11

**Question 3.Subtract the second polynomial from the first.i. x**

^{2}â€“ 9x + âˆš3 ; â€“ 19x + âˆš3 + 7x

^{2}ii. 2ab

^{2}+ 3a

^{2}b â€“ 4ab; 3ab â€“ 8ab

^{2}+ 2a

^{2}bSolution:

**Question 4.Multiply the given polynomials.i. 2x; x**
i. (2x) x (x

^{2}â€“ 2x â€“ 1ii. x

^{5}â€“ 1; x

^{3}+ 2x

^{2}+ 2iii. 2y +1; y

^{2}â€“ 2y + 3ySolution:

^{2}â€“ 2x â€“ 1) = 2x

^{3}â€“ 4x

^{2}â€“ 2x

ii. (x^{5} â€“ 1) Ã— (x^{3} + 2x^{2} + 2)

= x^{5} (x^{3} + 2x^{2} + 2) -1(x^{3} + 2x^{2} + 2)

= x^{8} + 2x^{7} + 2x^{5} â€“ x^{3} â€“ 2x^{2} â€“ 2

**Question 5.Divide first polynomial by second polynomial and write the answer in the form â€˜Dividend = Divisor x Quotient + Remainderâ€™.i. x**

^{3}â€“ 64; x â€“ 4ii. 5x

^{5}+ 4x

^{4}â€“ 3x

^{3}+ 2x

^{2}+ 2 ; x

^{2}â€“ xSolution:

i. x

^{3}â€“ 64 = x3 + 0x

^{2}+ 0x â€“ 64

âˆ´ Quotient = x

^{2}+ 4x + 16, Remainder = 0

Now, Dividend = Divisor x Quotient + Remainder

âˆ´ x

^{3}â€“ 64 = (x â€“ 4)(x

^{2}+ 4x + 16) + 0

ii. 5x^{5} + 4x^{4} â€“ 3x^{3} + 2x^{2} + 2 = 5x^{5} + 4x^{4} â€“ 3x^{3} + 2x + 0x + 2

âˆ´ Quotient = 5x^{3} + 9x^{2} + 6x + 8,

Remainder = 8x + 2

Now, Dividend = Divisor x Quotient + Remainder

âˆ´ 5x^{5} + 4x^{4} â€“ 3x^{3} + 2x^{2} + 2 = (x^{2} â€“ x)(5x^{3} + 9x^{2} + 6x + 8) + (8x + 2)

**Question 6.Write down the information in the form of algebraic expression and simplify.There is a rectangular farm with length (2a**

^{2}+ 3b

^{2}) metre and breadth (a

^{2}+ b

^{2}) metre. The farmer used a square shaped plot of the farm to build a house. The side of the plot was (a2 â€“ b2) metre. What is the area of the remaining part of the farm? [4 Marks]Solution: