Maths : Algebra: Book Back, Exercise, Example Numerical Question with Answers, Solution : Exercise 3.1: Polynomials

**Exercise 3.1**

**1. Which of the following expressions
are polynomials. If not give reason:**

**(i) 1/ x^{2} + 3x − 4 (ii) x^{2} (x − 1) (iii) 1/x (x + 5) (iv)
1/x^{-2} + 1/x^{-1} + 7 (v) √5 x^{2} + √3 x + √2 (vi) m^{2}
− ^{3}√m + 7m − 10 **

**2. Write the coefficient of x^{2}
and x in each of the following polynomials.**

**(i) 4 + 2/5 x^{2} − 3x (ii) 6 − 2x^{2} + 3x^{3}
− √7x (iii) πx^{2} − x + 2 (iv)
√3 x^{2} + √2 x + 0.5 (v) x^{2} – 7/2 x + 8**

**3. Find the degree of the following polynomials.**

**(i) 1 − √2 y^{2} + y^{7}
(ii) [ x^{3} − x^{4} + 6x^{6} ] / x^{2}
(iii) x^{3} ( x^{2} + x) (iv) 3x^{4} + 9x^{2} + 27x^{6} (v) 2√5 p^{4} − 8p^{3}/√3 + 2p^{2}/7**

**4. Rewrite the following polynomial in
standard form.**

**(i) x − 9 + √7x^{3} +
6x^{2} (ii) √2x^{2} – 7/2 x^{4} + x − 5x^{3} (iii) 7x^{3}
– 6/5 x^{2} + 4x − 1 (iv) y^{2} + √5y^{3} − 11 –
7/3y + 9y^{4} **

^{}

^{}

**5. Add the following polynomials and
find the degree of the resultant polynomial.**

**(i) p (x) = 6x^{2} − 7x + 2 ; q(x) = 6x^{3} − 7x + 15**

**(ii) h (x) = 7x^{3} − 6x + 1 ; f(x) = 7x^{2} + 17x − 9**

**(iii) f(x) = 16x^{4} − 5x^{2} + 9 ; g(x)
= − 6x^{3} + 7x – 15**

**6. Subtract the second polynomial from
the first polynomial and find the degree of the resultant polynomial.**

**(i)****
***p***(***x***) =**** 7 x^{2} + 6x
– 1 ; **

**(ii) f **

**(iii) h **

**7. What should be added to 2 x^{3}
+ 6x^{2} − 5x + 8 to get 3x^{3} − 2x^{2}
+ 6x + 15 ?**

**8. What must be subtracted from 2 x^{4}
+ 4x^{2} − 3x + 7 to get 3x^{3} − x^{2}
+ 2x + 1 ?**

**9. Multiply the following polynomials
and find the degree of the resultant polynomial:**

**(i) p **

**(ii) f
**

**(iii) h
**

**10. The cost of a chocolate is Rs. ( x
+ y) and Amir bought (x + y) chocolates. Find the total amount paid by
him in terms of x and y. If x =10, y =5 find the amount
paid by him.**

**11. The length of a rectangle is (3 x+2)
units and it’s breadth is (3x–2) units. Find its area in terms of x.
What will be the area if x = 20 units.**

*12. p ***(***x***) **

Tags : Numerical Problems with Answers, Solution | Algebra | Maths , 9th Maths : UNIT 3 : Algebra

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9th Maths : UNIT 3 : Algebra : Exercise 3.1: Polynomials | Numerical Problems with Answers, Solution | Algebra | Maths

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