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:
Representing the polynomial in first polynomial in coefficient form:
⟹ 1.x4 + 0.x3 – 3.x2 + 0.x – 8
⟹ (1, 0, -3, 0, -8)
So the final answer is written in the following form:
Quotient = x3 – 4x2 + 13x - 52
Remainder = 200
Question 6.
Divide each of the following polynomials by synthetic division method and also by linear division method. Write the quotient and the remainder.
(y3 – 3y2 + 5y – 1) ÷ (y – 1)
Answer:
The linear division is as follows:
Representing the polynomial in first polynomial in coefficient form:
⟹ 1.y3 – 3.y2 + 5.y – 1
⟹ (1, -3, 5, -1)
So, the final answer is written in the following form:
Quotient = y2 – 2y + 3
Remainder = 2
