Practice Set 3.3 Polynomials Class 9th Mathematics Part I MHB Solution

Polynomials

Class 9th Mathematics Part I MHB Solution

Practice Set 3.3

Question 1.

Divide each of the following polynomials by synthetic division method and also by linear division method. Write the quotient and the remainder.

(2m2 – 3m + 10) ÷ (m – 5)


Answer:

The linear division method is as follows:



Representing the polynomial in first polynomial in coefficient form:


⟹ 2.m2 – 3.m + 10


⟹ (2, – 3, 10)



Bring the first term as it is. Then multiply 5 with the value written in the bottom result area. Continue this until done.


Quotient = 2m + 7


Remainder = 45



Question 2.

Divide each of the following polynomials by synthetic division method and also by linear division method. Write the quotient and the remainder.

(x4 + 2x3 + 3x2 + 4x +5) ÷ (x + 2)


Answer:

The linear division is as follows:



Representing the polynomial in first polynomial in coefficient form:


⟹ 1.x4 + 2.x3 + 3x2 + 4x + 5


⟹ (1 2 3 4 5)



So the final answer is written in the following form:


Quotient = x3 + 3x – 2


Remainder = 9



Question 3.

Divide each of the following polynomials by synthetic division method and also by linear division method. Write the quotient and the remainder.

(y3 – 216) ÷ (y – 6)


Answer:

The linear division method is as follows:



Representing the polynomial in first polynomial in coefficient form:


⟹ 1.y3 + 0.y2 + 0.y – 216


⟹ (1, 0, 0, -216)



So the final answer is written in the following form:


Quotient = y2 + 6y + 36


Remainder = 0



Question 4.

Divide each of the following polynomials by synthetic division method and also by linear division method. Write the quotient and the remainder.

(2x4 + 3x3 + 4x - 2x2) ÷ (x+3)


Answer:

The linear division is as follows:



Representing the polynomial in first polynomial in coefficient form:


⟹ 2.x4 + 3.x3 – 2.x2 + 4.x


⟹ (2, 3, -2, 4, 0)



So, the final answer is written in the following form:


Quotient = 2x3 – 3x2 + 7x – 17


Remainder = 51



Question 5.

Divide each of the following polynomials by synthetic division method and also by linear division method. Write the quotient and the remainder.

(x4 – 3x2 – 8) ÷ (x+4)


Answer:

The linear division is as follows: