In this blogpost we will discuss Class 9 Chapter 2: Polynomials Worksheet for Exams in detail all the important questions
1. Multiple Choice Questions (MCQs):
- Which of the following is a polynomial?
- (a) 3x + 2
- (b) 2/x + 5
- (c) 3x^2 + √x
- (d) 5/x + 7
Explanation: A polynomial is an algebraic expression with non-negative integer powers of the variable. So, option (a) is a polynomial. - The degree of the polynomial 5x^3 + 4x^2 + 2x + 1 is:
- (a) 3
- (b) 4
- (c) 2
- (d) 1
Explanation: The degree of a polynomial is the highest power of the variable. Here, the highest power is 3 (in 5x^3). - What is the value of x in the polynomial 2x^2 – 3x + 5 = 0?
- (a) 2
- (b) -2
- (c) 3
- (d) Cannot be determined
Explanation: To find the roots, we would need to use the quadratic formula. The roots depend on the discriminant, which we do not have in this case. - Which of the following is a binomial?
- (a) x + 1
- (b) x^2 – 3x + 2
- (c) 3x^2 + 2x
- (d) 5x^3
Explanation: A binomial has two terms. The expression x + 1 has two terms, so it’s a binomial. - The polynomial 4x^3 + 6x^2 – 7x + 3 is a:
- (a) Monomial
- (b) Binomial
- (c) Trinomial
- (d) None of the above
Explanation: A trinomial is a polynomial with three terms, and 4x^3 + 6x^2 – 7x + 3 has four terms.
2. Short Answer Type Questions:
- Define a polynomial and give an example.Answer:
A polynomial is an algebraic expression consisting of terms with non-negative integer exponents of the variable.
Example: 3×2+4x+53x^2 + 4x + 53×2+4x+5 is a polynomial of degree 2. - What is the degree of the polynomial 4x^4 + 3x^2 + 7x + 8?Answer:
The degree of a polynomial is the highest power of the variable.
Here, the highest power is 4, so the degree is 4. - Find the value of the polynomial p(x)=2×2+3x−5p(x) = 2x^2 + 3x – 5p(x)=2×2+3x−5 at x = 3.Answer:
Substituting x = 3 in the polynomial:
p(3)=2(3)2+3(3)−5p(3) = 2(3)^2 + 3(3) – 5p(3)=2(3)2+3(3)−5
p(3)=2(9)+9−5=18+9−5=22p(3) = 2(9) + 9 – 5 = 18 + 9 – 5 = 22p(3)=2(9)+9−5=18+9−5=22 - Write the polynomial obtained by adding 3x^2 – 2x + 4 and 2x^2 + 3x – 7.Answer:
Add the like terms:
(3×2+2×2)+(−2x+3x)+(4−7)(3x^2 + 2x^2) + (-2x + 3x) + (4 – 7)(3×2+2×2)+(−2x+3x)+(4−7)
=5×2+x−3= 5x^2 + x – 3=5×2+x−3
So, the polynomial is 5x^2 + x – 3. - Subtract the polynomial 3×2−5x+43x^2 – 5x + 43×2−5x+4 from 6×2+7x−26x^2 + 7x – 26×2+7x−2.Answer:
Subtract the like terms:
(6×2−3×2)+(7x+5x)+(−2−4)(6x^2 – 3x^2) + (7x + 5x) + (-2 – 4)(6×2−3×2)+(7x+5x)+(−2−4)
=3×2+12x−6= 3x^2 + 12x – 6=3×2+12x−6
So, the result is 3x^2 + 12x – 6.
3. Long Answer Type Questions:
- Factorize the polynomial x2−5x+6x^2 – 5x + 6×2−5x+6.Answer:
We need to factor the quadratic equation. We find two numbers that multiply to 6 and add to -5, which are -2 and -3.
Therefore,
x2−5x+6=(x−2)(x−3)x^2 – 5x + 6 = (x – 2)(x – 3)x2−5x+6=(x−2)(x−3). - Factorize the polynomial 4×2−254x^2 – 254×2−25.Answer:
This is a difference of squares:
4×2−25=(2x)2−524x^2 – 25 = (2x)^2 – 5^24×2−25=(2x)2−52.
Using the formula a2−b2=(a−b)(a+b)a^2 – b^2 = (a – b)(a + b)a2−b2=(a−b)(a+b), we get:
(2x−5)(2x+5)(2x – 5)(2x + 5)(2x−5)(2x+5). - Factorize the polynomial x2+7x+10x^2 + 7x + 10×2+7x+10.Answer:
We need two numbers that multiply to 10 and add to 7, which are 2 and 5.
Therefore,
x2+7x+10=(x+2)(x+5)x^2 + 7x + 10 = (x + 2)(x + 5)x2+7x+10=(x+2)(x+5). - Divide 3×3−5×2+2x−43x^3 – 5x^2 + 2x – 43×3−5×2+2x−4 by x−1x – 1x−1 using synthetic division.Answer:
To divide using synthetic division, set up the division with the divisor x−1x – 1x−1 and the coefficients of the polynomial.
The steps lead to the quotient and remainder. The quotient is 3×2−2x+23x^2 – 2x + 23×2−2x+2, and the remainder is -2. - Find the remainder when 3×3−5×2+2x−43x^3 – 5x^2 + 2x – 43×3−5×2+2x−4 is divided by x−2x – 2x−2.Answer:
Use the remainder theorem:
Substitute x=2x = 2x=2 in the polynomial:
3(2)3−5(2)2+2(2)−43(2)^3 – 5(2)^2 + 2(2) – 43(2)3−5(2)2+2(2)−4
=3(8)−5(4)+4−4= 3(8) – 5(4) + 4 – 4=3(8)−5(4)+4−4
=24−20+4−4=4= 24 – 20 + 4 – 4 = 4=24−20+4−4=4.
So, the remainder is 4.
4. Word Problems:
- The product of two consecutive positive integers is 306. What are the integers?Answer:
Let the integers be xxx and x+1x+1x+1.
Their product is x(x+1)=306x(x+1) = 306x(x+1)=306.
Solving x2+x−306=0x^2 + x – 306 = 0x2+x−306=0, we factorize to get:
(x−17)(x+18)=0(x – 17)(x + 18) = 0(x−17)(x+18)=0,
so x=17x = 17x=17. The integers are 17 and 18. - A rectangular field has a length of 3x+23x + 23x+2 meters and a width of x−1x – 1x−1 meters. Find the area of the field.Answer:
The area of the rectangle is given by:
Area=Length×Width\text{Area} = \text{Length} \times \text{Width}Area=Length×Width.
So,
Area=(3x+2)(x−1)\text{Area} = (3x + 2)(x – 1)Area=(3x+2)(x−1).
Expanding:
=3×2−3x+2x−2=3×2−x−2= 3x^2 – 3x + 2x – 2 = 3x^2 – x – 2=3×2−3x+2x−2=3×2−x−2.
So, the area is 3×2−x−23x^2 – x – 23×2−x−2 square meters. - The sum of two polynomials 2×2−3x+42x^2 – 3x + 42×2−3x+4 and x2+5x−6x^2 + 5x – 6×2+5x−6 is:Answer:
Add the like terms:
(2×2+x2)+(−3x+5x)+(4−6)(2x^2 + x^2) + (-3x + 5x) + (4 – 6)(2×2+x2)+(−3x+5x)+(4−6)
=3×2+2x−2= 3x^2 + 2x – 2=3×2+2x−2.
So, the sum is 3x^2 + 2x – 2. - The product of two polynomials x+3x + 3x+3 and x−2x – 2x−2 is:Answer:
Multiply the two polynomials using distributive property:
(x+3)(x−2)=x2−2x+3x−6=x2+x−6(x + 3)(x – 2) = x^2 – 2x + 3x – 6 = x^2 + x – 6(x+3)(x−2)=x2−2x+3x−6=x2+x−6.
So, the product is x^2 + x – 6. - Find the zeros of the polynomial x2−5x+6x^2 – 5x + 6×2−5x+6.Answer:
Factorize the polynomial:
x2−5x+6=(x−2)(x−3)x^2 – 5x + 6 = (x – 2)(x – 3)x2−5x+6=(x−2)(x−3).
The zeros of the polynomial are x=2x = 2x=2 and x=3x = 3x=3.
Here are 30 additional questions related to Chapter 2: Polynomials for Class 9 Maths, which will cover various concepts from this chapter.
1. Multiple Choice Questions (MCQs):
- Which of the following is a polynomial?
- (a) x−1+5x^{-1} + 5x−1+5
- (b) 2×2+3x+42x^2 + 3x + 42×2+3x+4
- (c) 3×1/2+73x^{1/2} + 73×1/2+7
- (d) 1x+6\frac{1}{x} + 6×1+6
- The degree of the polynomial 7×4−2×3+3×2+57x^4 – 2x^3 + 3x^2 + 57×4−2×3+3×2+5 is:
- (a) 4
- (b) 3
- (c) 2
- (d) 5
- Which of the following is a monomial?
- (a) 4×3+3×2−2x4x^3 + 3x^2 – 2x4x3+3×2−2x
- (b) 7x7x7x
- (c) x2+x+1x^2 + x + 1×2+x+1
- (d) 3×2+2x+43x^2 + 2x + 43×2+2x+4
- The polynomial 2×3−5×2+3x−72x^3 – 5x^2 + 3x – 72×3−5×2+3x−7 has how many terms?
- (a) 4
- (b) 3
- (c) 2
- (d) 1
- Which of the following is a quadratic polynomial?
- (a) 4x+74x + 74x+7
- (b) 5×2+3x−25x^2 + 3x – 25×2+3x−2
- (c) 7×3+4x27x^3 + 4x^27×3+4×2
- (d) 2×5+3x42x^5 + 3x^42×5+3×4
2. Short Answer Type Questions:
- Find the degree of the polynomial 9×5−3×2+79x^5 – 3x^2 + 79×5−3×2+7.
- Express the polynomial 5×2−3x+65x^2 – 3x + 65×2−3x+6 in standard form.
- Factorize the polynomial x2+8x+15x^2 + 8x + 15×2+8x+15.
- Find the value of p(x)=x2−4x+3p(x) = x^2 – 4x + 3p(x)=x2−4x+3 at x=2x = 2x=2.
- Subtract 3×2+5x−73x^2 + 5x – 73×2+5x−7 from 5×2−3x+25x^2 – 3x + 25×2−3x+2.
3. Long Answer Type Questions:
- Factorize 4×2+12x4x^2 + 12x4x2+12x.
- Solve x2+6x+8=0x^2 + 6x + 8 = 0x2+6x+8=0 by factorization.
- Find the quotient when 6×3−4×2+5x−86x^3 – 4x^2 + 5x – 86×3−4×2+5x−8 is divided by x−2x – 2x−2 using synthetic division.
- Find the sum of the polynomials 4×2+3x−24x^2 + 3x – 24×2+3x−2 and 5×2−2x+75x^2 – 2x + 75×2−2x+7.
- Multiply 3x+53x + 53x+5 by x2−4x+7x^2 – 4x + 7×2−4x+7.
4. Word Problems:
- A polynomial x2−6x+9x^2 – 6x + 9×2−6x+9 represents the area of a square. Find the side length of the square.
- The cost of a product is given by 5×2+3x+75x^2 + 3x + 75×2+3x+7 where xxx represents the number of units purchased. Find the total cost if x=4x = 4x=4.
- A farmer has a rectangular plot with length 2x+32x + 32x+3 and width x−1x – 1x−1. Find the area of the plot.
- The sum of the length and width of a rectangle is 2x+72x + 72x+7. If the area is given by 3×2+13x+103x^2 + 13x + 103×2+13x+10, find the width of the rectangle.
- The perimeter of a rectangle is given by 2x+102x + 102x+10 and its length is 3x−53x – 53x−5. Find its width.
5. Factorization and Simplification:
- Factorize the polynomial 3×2−6x3x^2 – 6x3x2−6x.
- Factorize x2−9x+20x^2 – 9x + 20×2−9x+20.
- Factorize x2+12x+36x^2 + 12x + 36×2+12x+36.
- Factorize x2−5x−14x^2 – 5x – 14×2−5x−14.
- Factorize 2×2+5x−32x^2 + 5x – 32×2+5x−3.
6. More Operations with Polynomials:
- Divide the polynomial 3×3−5×2+6x−73x^3 – 5x^2 + 6x – 73×3−5×2+6x−7 by x−1x – 1x−1 using synthetic division.
- Multiply (x−2)(x – 2)(x−2) by (x2+4x+4)(x^2 + 4x + 4)(x2+4x+4).
- Divide 4×3+6×2−8x+24x^3 + 6x^2 – 8x + 24×3+6×2−8x+2 by 2x+12x + 12x+1.
- Subtract 7×3+6×2−5x+47x^3 + 6x^2 – 5x + 47×3+6×2−5x+4 from 9×3−4×2+3x−29x^3 – 4x^2 + 3x – 29×3−4×2+3x−2.
- Simplify the expression 3×2+7x−5x+2\frac{3x^2 + 7x – 5}{x + 2}x+23×2+7x−5 by performing polynomial long division.
These 30 additional questions cover topics like polynomial operations, factorization, degree, and simplification. They also include both basic and advanced questions, helping to improve your understanding and problem-solving skills in Polynomials. If you need solutions or further explanations, feel free to ask!
Below are these questions solved in detail;
1. Multiple Choice Questions (MCQs):
- Which of the following is a polynomial?
- Answer: (b) 2×2+3x+42x^2 + 3x + 42×2+3x+4
Explanation: A polynomial has non-negative integer exponents of the variable, so this is a valid polynomial.
- Answer: (b) 2×2+3x+42x^2 + 3x + 42×2+3x+4
- The degree of the polynomial 7×4−2×3+3×2+57x^4 – 2x^3 + 3x^2 + 57×4−2×3+3×2+5 is:
- Answer: (a) 4
Explanation: The degree is the highest power of the variable. Here, the highest power is x4x^4×4.
- Answer: (a) 4
- Which of the following is a monomial?
- Answer: (b) 7x7x7x
Explanation: A monomial has only one term. 7x7x7x is a monomial because it has only one term.
- Answer: (b) 7x7x7x
- The polynomial 2×3−5×2+3x−72x^3 – 5x^2 + 3x – 72×3−5×2+3x−7 has how many terms?
- Answer: (a) 4
Explanation: The given polynomial has four terms: 2x32x^32×3, −5×2-5x^2−5×2, 3x3x3x, and −7-7−7.
- Answer: (a) 4
- Which of the following is a quadratic polynomial?
- Answer: (b) 5×2+3x−25x^2 + 3x – 25×2+3x−2
Explanation: A quadratic polynomial has a degree of 2, and 5×2+3x−25x^2 + 3x – 25×2+3x−2 has the highest degree 2.
- Answer: (b) 5×2+3x−25x^2 + 3x – 25×2+3x−2
2. Short Answer Type Questions:
- Find the degree of the polynomial 9×5−3×2+79x^5 – 3x^2 + 79×5−3×2+7.Answer:
The degree of the polynomial is the highest power of xxx, which is 555.
So, the degree is 5. - Express the polynomial 5×2−3x+65x^2 – 3x + 65×2−3x+6 in standard form.Answer:
The standard form of a polynomial is written with terms in descending powers of xxx.
The given polynomial is already in standard form:
5×2−3x+65x^2 – 3x + 65×2−3x+6. - Factorize the polynomial x2+8x+15x^2 + 8x + 15×2+8x+15.Answer:
We need to find two numbers that multiply to 15 and add to 8. These numbers are 3 and 5.
Therefore, the factorization is:
x2+8x+15=(x+3)(x+5)x^2 + 8x + 15 = (x + 3)(x + 5)x2+8x+15=(x+3)(x+5). - Find the value of p(x)=x2−4x+3p(x) = x^2 – 4x + 3p(x)=x2−4x+3 at x=2x = 2x=2.Answer:
Substituting x=2x = 2x=2 into the polynomial:
p(2)=(2)2−4(2)+3p(2) = (2)^2 – 4(2) + 3p(2)=(2)2−4(2)+3
p(2)=4−8+3=−1p(2) = 4 – 8 + 3 = -1p(2)=4−8+3=−1.
So, p(2)=−1p(2) = -1p(2)=−1. - Subtract 3×2+5x−73x^2 + 5x – 73×2+5x−7 from 5×2−3x+25x^2 – 3x + 25×2−3x+2.Answer:
Subtracting the polynomials:
(5×2−3x+2)−(3×2+5x−7)(5x^2 – 3x + 2) – (3x^2 + 5x – 7)(5×2−3x+2)−(3×2+5x−7)
=5×2−3x+2−3×2−5x+7= 5x^2 – 3x + 2 – 3x^2 – 5x + 7=5×2−3x+2−3×2−5x+7
=(5×2−3×2)+(−3x−5x)+(2+7)= (5x^2 – 3x^2) + (-3x – 5x) + (2 + 7)=(5×2−3×2)+(−3x−5x)+(2+7)
=2×2−8x+9= 2x^2 – 8x + 9=2×2−8x+9.
So, the result is 2×2−8x+92x^2 – 8x + 92×2−8x+9.
3. Long Answer Type Questions:
- Factorize 4×2+12x4x^2 + 12x4x2+12x.Answer:
Factor out the greatest common factor, which is 4x4x4x:
4×2+12x=4x(x+3)4x^2 + 12x = 4x(x + 3)4×2+12x=4x(x+3). - Solve x2+6x+8=0x^2 + 6x + 8 = 0x2+6x+8=0 by factorization.Answer:
To factorize, we find two numbers that multiply to 8 and add to 6. These are 4 and 2.
So, the factorization is:
x2+6x+8=(x+4)(x+2)x^2 + 6x + 8 = (x + 4)(x + 2)x2+6x+8=(x+4)(x+2).
Setting each factor equal to 0:
x+4=0x + 4 = 0x+4=0 or x+2=0x + 2 = 0x+2=0.
So, x=−4x = -4x=−4 or x=−2x = -2x=−2. - Find the quotient when 6×3−4×2+5x−86x^3 – 4x^2 + 5x – 86×3−4×2+5x−8 is divided by x−2x – 2x−2 using synthetic division.Answer:
Using synthetic division, we divide 6×3−4×2+5x−86x^3 – 4x^2 + 5x – 86×3−4×2+5x−8 by x−2x – 2x−2, and the quotient is:
6×2+8x+216x^2 + 8x + 216×2+8x+21 with a remainder of 34. - Find the sum of the polynomials 4×2+3x−24x^2 + 3x – 24×2+3x−2 and 5×2−2x+75x^2 – 2x + 75×2−2x+7.Answer:
Add the like terms:
(4×2+5×2)+(3x−2x)+(−2+7)(4x^2 + 5x^2) + (3x – 2x) + (-2 + 7)(4×2+5×2)+(3x−2x)+(−2+7)
=9×2+x+5= 9x^2 + x + 5=9×2+x+5.
So, the sum is 9×2+x+59x^2 + x + 59×2+x+5. - Multiply 3x+53x + 53x+5 by x2−4x+7x^2 – 4x + 7×2−4x+7.Answer:
Use the distributive property to multiply:
(3x+5)(x2−4x+7)(3x + 5)(x^2 – 4x + 7)(3x+5)(x2−4x+7)
=3x(x2−4x+7)+5(x2−4x+7)= 3x(x^2 – 4x + 7) + 5(x^2 – 4x + 7)=3x(x2−4x+7)+5(x2−4x+7)
=3×3−12×2+21x+5×2−20x+35= 3x^3 – 12x^2 + 21x + 5x^2 – 20x + 35=3×3−12×2+21x+5×2−20x+35
=3×3−7×2+x+35= 3x^3 – 7x^2 + x + 35=3×3−7×2+x+35.
So, the product is 3×3−7×2+x+353x^3 – 7x^2 + x + 353×3−7×2+x+35.
4. Word Problems:
- A polynomial x2−6x+9x^2 – 6x + 9×2−6x+9 represents the area of a square. Find the side length of the square.Answer:
The area of the square is x2−6x+9x^2 – 6x + 9×2−6x+9, which is a perfect square trinomial.
We can rewrite this as (x−3)2(x – 3)^2(x−3)2, so the side length is x−3x – 3x−3. - The cost of a product is given by 5×2+3x+75x^2 + 3x + 75×2+3x+7 where xxx represents the number of units purchased. Find the total cost if x=4x = 4x=4.Answer:
Substituting x=4x = 4x=4 into the polynomial:
5(4)2+3(4)+7=5(16)+12+7=80+12+7=995(4)^2 + 3(4) + 7 = 5(16) + 12 + 7 = 80 + 12 + 7 = 995(4)2+3(4)+7=5(16)+12+7=80+12+7=99.
So, the total cost is 99. - A farmer has a rectangular plot with length 2x+32x + 32x+3 and width x−1x – 1x−1. Find the area of the plot.Answer:
The area of the rectangle is given by:
Area=Length×Width=(2x+3)(x−1)\text{Area} = \text{Length} \times \text{Width} = (2x + 3)(x – 1)Area=Length×Width=(2x+3)(x−1).
Expanding:
=2×2−2x+3x−3=2×2+x−3= 2x^2 – 2x + 3x – 3 = 2x^2 + x – 3=2×2−2x+3x−3=2×2+x−3.
So, the area is 2×2+x−32x^2 + x – 32×2+x−3. - The sum of the length and width of a rectangle is 2x+72x + 72x+7. If the area is given by 3×2+13x+103x^2 + 13x + 103×2+13x+10, find the width of the rectangle.Answer:
Let the length be 2x+72x + 72x+7 and the width be www.
The area is given by Area=Length×Width\text{Area} = \text{Length} \times \text{Width}Area=Length×Width, so:
(2x+7)×w=3×2+13x+10(2x + 7) \times w = 3x^2 + 13x + 10(2x+7)×w=3×2+13x+10.
Solving for www:
w=3×2+13x+102x+7w = \frac{3x^2 + 13x + 10}{2x + 7}w=2x+73×2+13x+10.
After dividing, we get:
w=3x+3w = 3x + 3w=3x+3.
So, the width is 3x+33x + 33x+3. - The perimeter of a rectangle is given by 2x+102x + 102x+10 and its length is 3x−53x – 53x−5. Find its width.Answer:
The perimeter of a rectangle is 2(Length+Width)2(\text{Length} + \text{Width})2(Length+Width).
So, 2((3x−5)+w)=2x+102((3x – 5) + w) = 2x + 102((3x−5)+w)=2x+10.
Simplifying:
6x−10+2w=2x+106x – 10 + 2w = 2x + 106x−10+2w=2x+10
2w=−4x+202w = -4x + 202w=−4x+20
w=−2x+10w = -2x + 10w=−2x+10.
So, the width is −2x+10-2x + 10−2x+10.
5. Factorization and Simplification:
- Factorize the polynomial 3×2−6x3x^2 – 6x3x2−6x.Answer:
Factor out the greatest common factor:
3x(x−2)3x(x – 2)3x(x−2). - Factorize x2−9x+20x^2 – 9x + 20×2−9x+20.Answer:
We need two numbers that multiply to 20 and add to -9, which are -4 and -5.
Therefore, the factorization is:
(x−4)(x−5)(x – 4)(x – 5)(x−4)(x−5). - Factorize x2+12x+36x^2 + 12x + 36×2+12x+36.Answer:
This is a perfect square trinomial:
(x+6)2(x + 6)^2(x+6)2. - Factorize x2−5x−14x^2 – 5x – 14×2−5x−14.Answer:
We need two numbers that multiply to -14 and add to -5, which are -7 and 2.
So, the factorization is:
(x−7)(x+2)(x – 7)(x + 2)(x−7)(x+2). - Factorize 2×2+5x−32x^2 + 5x – 32×2+5x−3.Answer:
The two numbers that multiply to 2×−3=−62 \times -3 = -62×−3=−6 and add to 5 are 6 and -1.
The factorization is:
2×2+6x−x−3=2x(x+3)−1(x+3)=(2x−1)(x+3)2x^2 + 6x – x – 3 = 2x(x + 3) – 1(x + 3) = (2x – 1)(x + 3)2×2+6x−x−3=2x(x+3)−1(x+3)=(2x−1)(x+3).
6. More Operations with Polynomials:
- Divide the polynomial 3×3−5×2+6x−73x^3 – 5x^2 + 6x – 73×3−5×2+6x−7 by x−1x – 1x−1 using synthetic division Answer:
The quotient is 3×2−2x+43x^2 – 2x + 43×2−2x+4 with a remainder of −3-3−3. - Multiply (x−2)(x – 2)(x−2) by (x2+4x+4)(x^2 + 4x + 4)(x2+4x+4).Answer:
(x−2)(x2+4x+4)=x3+4×2+4x−2×2−8x−8=x3+2×2−4x−8(x – 2)(x^2 + 4x + 4) = x^3 + 4x^2 + 4x – 2x^2 – 8x – 8 = x^3 + 2x^2 – 4x – 8(x−2)(x2+4x+4)=x3+4×2+4x−2×2−8x−8=x3+2×2−4x−8. - Divide 4×3+6×2−8x+24x^3 + 6x^2 – 8x + 24×3+6×2−8x+2 by 2x+12x + 12x+1.Answer:
The quotient is 2×2+2x−42x^2 + 2x – 42×2+2x−4 with a remainder of 000. - Subtract 7×3+6×2−5x+47x^3 + 6x^2 – 5x + 47×3+6×2−5x+4 from 9×3−4×2+3x−29x^3 – 4x^2 + 3x – 29×3−4×2+3x−2.Answer:
(9×3−4×2+3x−2)−(7×3+6×2−5x+4)(9x^3 – 4x^2 + 3x – 2) – (7x^3 + 6x^2 – 5x + 4)(9×3−4×2+3x−2)−(7×3+6×2−5x+4)
=(9×3−7×3)+(−4×2−6×2)+(3x+5x)+(−2−4)= (9x^3 – 7x^3) + (-4x^2 – 6x^2) + (3x + 5x) + (-2 – 4)=(9×3−7×3)+(−4×2−6×2)+(3x+5x)+(−2−4)
=2×3−10×2+8x−6= 2x^3 – 10x^2 + 8x – 6=2×3−10×2+8x−6. - Simplify the expression 3×2+7x−5x+2\frac{3x^2 + 7x – 5}{x + 2}x+23×2+7x−5 by performing polynomial long division.Answer:
The quotient is 3x+13x + 13x+1 with a remainder of −7-7−7.
So, the simplified expression is 3x+1+−7x+23x + 1 + \frac{-7}{x + 2}3x+1+x+2−7.
These are the solutions for the 30 questions in Chapter 2 on Polynmials. Let me know if you need any further clarifications!
Class 9 Maths Chapter 1: Numbers Systems – Detailed Solutions to All Exercises
For more Updates Click Here.
As a seasoned content writer specialized in the fitness and health niche, Arun Bhagat has always wanted to promote wellness. After gaining proper certification as a gym trainer with in-depth knowledge of virtually all the information related to it, he exercised his flair for writing interesting, informative content to advise readers on their healthier lifestyle. His topics range from workout routines, nutrition, and mental health to strategies on how to be more fit in general. His writing is informative but inspiring for people to achieve their wellness goals as well. Arun is committed to equipping those he reaches with the insights and knowledge gained through fitness.