Home › Worksheets › CBSE Grade 9 Math › Polynomials Prepared by Mohsim Digital Education
Name: _________________________
Date: _________________________
Score: _______ / 40
The polynomial 5x³ − 3x² + x − 7 has degree 3, and x³ + 3x² + 1 is the polynomial listed, so this Class 9 sheet opens with the degree count and one valid polynomial. The key records −3 as a value and x² − 9 as a polynomial product.
Key Takeaways
5x³ − 3x² + x − 7 has degree 3 (Q1).
x³ + 3x² + 1 is a polynomial (Q2).
Q5 records x² − 9 as an answer.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.
The degree of the polynomial 5x³ - 3x² + x - 7 is
(a) 1 (b) 2 (c) 3 (d) 4
2.
Which of the following is a polynomial?
(a) x² + √x (b) √x + 1 (c) x³ + 3x² + 1 (d) x + 2/x
3.
The zero of the polynomial p(x) = 2x + 6 is
(a) -3 (b) 3 (c) -6 (d) 6
4.
The remainder when x³ + 1 is divided by x + 1 is
(a) 0 (b) 1 (c) 2 (d) -1
5.
The product (x + 3)(x - 3) is equal to
(a) x² - 9 (b) x² + 9 (c) x² - 6x + 9 (d) x² + 6x + 9
6.
If p(x) = x² - 3x + 2, then p(2) is equal to
(a) 0 (b) 1 (c) 2 (d) 4
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.
Write the degree of the polynomial x³ - x² + 5.
8.
Check whether -1 is a zero of the polynomial p(x) = x³ + 1.
9.
Find the value of the polynomial p(x) = x² - 5x + 6 at x = 0.
10.
Using the remainder theorem, find the remainder when x² + 1 is divided by x - 1.
11.
State the zeroes of the polynomial p(x) = x² - 4.
12.
Expand (x + 5)² using the identity (a + b)² = a² + 2ab + b².
13.
Factorise x² - 9.
14.
Write the coefficient of x² in the polynomial 2 + x + x³ - 3x².
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.
The area of a rectangle is (x² + 5x + 6) sq units and its breadth is (x + 2) units. Find its length.
16.
The volume of a cuboid is (x³ + 1) cubic units and one of its edges is (x + 1) units. Find the product of the other two dimensions.
17.
The area of a square is (x² + 2x + 1) sq units. Find the side of the square in terms of x.
18.
Check whether (x + 1) is a factor of the polynomial p(x) = 2x³ + x² - 2x - 1 by evaluating p(-1).
19.
There are (x + 2) rows in a garden and (x - 2) plants in each row. Find the total number of plants in the garden.
20.
A shopkeeper sold 105 shirts at ₹95 each. Find the total amount received using a suitable identity.
Answer Key
1. c) 3
2. c) x³ + 3x² + 1
3. a) -3
4. a) 0
5. a) x² - 9
6. a) 0
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the degree of 5x³ − 3x² + x − 7?
3, option (c) in this worksheet (Q1).
Which of these is a polynomial?
x³ + 3x² + 1, option (c) in this worksheet (Q2).
What is (x − 3)(x + 3)?
x² − 9, option (a) in this worksheet (Q5).