Class 9th Polynomial

 

 

GRADE: IX

      

 TOPIC: POLYNOMIALS

 

PART-A

1. Write the degree of the polynomials

(i) (3x² ‒5x+6) (x‒2)                 (ii) (x⁸ ‒ 1) (x⁸ + 1)

2.  Find p(0), p(1), p(‒2) for the polynomial p(y) = (y+2) (y‒2)

3.  If p(x) = x² ‒ 4x + 3, evaluate p(2) - p(‒1) + p()

4.  Find the zeroes of the polynomial  p(x) = (x‒2)² ‒ (x+2)²

5.  Show that 5 is a zero of polynomial 2𝑥³ − 7𝑥² − 16𝑥 + 5.

6.  If 𝑥 + 1 is a factor of 𝑎𝑥³ + 𝑥² − 2𝑥 + 4𝑎 − 9, find the value of a.

7.  Factorise 

(i) 2x² ‒5x + 3                                       (ii) 2x² ‒ x‒3                           (iii) 9x² – 12x + 4 

8. Find the value of k.

(i)     If 𝑥 − 2 is a factor of the polynomial 4𝑥³ + 3𝑥² − 4𝑥 + 𝑘.

(ii)   If 𝑥 + 1 is a factor of the polynomial 2𝑥² + 𝑘𝑥.

11.Case Study Question

Read the text carefully and answer the questions:

To recapitulate the concept of polynomials a teacher bought a box with some slips of polynomials written on them in the class. She asked the students to pick up a slip turn wise and say any four lines about the polynomial written on it. Based on above information answer the following questions.

(i)     (a) The polynomial written on Aparajita’s slip was 𝑝(𝑡) = 4𝑡² − 9 + 𝑡. What is the value of 𝑝(2)?

(b)   Saanvi got the polynomial 𝑝(𝑥) = 1 − 𝑥². What type of polynomial is it?

(ii)   (a) Varun got the polynomial 𝑝(𝑥) = 𝑦² − 5𝑦 + 6, calculate the value of 𝑝(−1).

(b)   One of the slips had polynomial 𝑥² − 6𝑥 + 9 written on it. Write its factors  

PART-B MULTIPLE CHOICE QUESTIONS

1.The coefficient of x in the expansion of (x + 3)³ is

(a) 1                                   (b) 9                       (c) 18                           (d) 27

2.The degree of the polynomial  is 

(a) 2                                   (b) 0                       (c) 1                              (d)  

3. One of the zeroes of the polynomial 2x² + 7x – 4 is

(a) 2                                    (b)                         (c) −                        (d) – 2 

4. The degree of the constant polynomial is
(a) 1                                   (b) 2                       (c) 3       5. If 𝑝(𝑥) = 𝑥 + 3,  then 𝑝(𝑥) + 𝑝(−𝑥) is equal to		(d) 0
(a) 3                                   (b) 2x                     (c) 0       6. Which of the following is not a polynomial?		(d) 6

(^{a) 3}x³ +6x² ₋ ¹ x−8                  (b) 9x² − +4x      2          (c) 𝑥 + ³               (d) 3x² ₋2 3 5x₊

         2                                                                      2𝑥

7. A linear polynomial 

(a) May have one zero                                      (b) has one and only one zero           (c) May have two zero                                    (d) May have more than one zero

8. Zero of the zero polynomial is  

(a) 0                             (b) 1                              (c) any real number                (d) Not defined

9. Assertion (A): If 𝑓(𝑥) = 3𝑥⁷ − 4𝑥⁶ + 𝑥 + 9 is a polynomial, then its degree is 7.

Reason(R): Degree of a polynomial is the highest power of the variable in it.

(a) Both A and R are true and R is the correct explanation of A        (b) Both A and Rare true but R is not the correct explanation of A.

(c)   A is true but R is false                    

(d)  A is false but R is true. 

10. Assertion (A): If  𝑥 + 7 is a factor of  f(x) = 𝑥² + 11𝑥 − 2𝑎, then 𝑎 = −14

Reason(R): If 𝑥 + 𝑎 is a factor of a polynomial, then 𝑓(𝑎) = 0 (a) Both A and R are true and R is the correct explanation of A             (b) Both A and Rare true but R is not the correct explanation of A.

(c)   A is true but R is false                    

(d)  A is false but R is true.