NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3 are part ofÂ NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3.

- Polynomials Class 10 Ex 2.1
- Polynomials Class 10 Ex 2.2
- Polynomials Class 10 Ex 2.3
- Polynomials Class 10 Ex 2.4

Board | CBSE |

Textbook | NCERT |

Class | Class 10 |

Subject | Maths |

Chapter | Chapter 2 |

Polynomials | |

Exercise | Ex 2.3 |

Number of Questions Solved | 5 |

Category | NCERT Solutions |

## NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.3

**Ex 2.3 Class 10 Maths Question 1.**Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

**(i)**Â p(x) = x

^{3}Â â€“ 3x

^{2}Â + 5x â€“ 3, g(x) = x

^{2}Â â€“ 2

**(ii)**Â p(x) = x

^{4}Â â€“ 3x

^{2}Â + 4x + 5, g(x) = x

^{2}Â + 1 â€“ x

**(iii)**Â p(x) = x

^{4}â€“ 5x + 6, g(x) = 2 â€“ x

^{2}

**Solution:**

**Ex 2.3 Class 10 MathsÂ Question 2.**Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.

**(i)**Â t

^{2}Â â€“ 3, 2t

^{4}Â + 3t

^{3}Â â€“ 2t

^{2}â€“ 9t â€“ 12

**(ii)**Â x

^{2}Â + 3x + 1, 3x

^{4}Â + 5x

^{3}Â â€“ 7x

^{2}Â + 2x + 2

**(iii)**Â x

^{2}Â + 3x + 1, x

^{5}Â â€“ 4x

^{3Â }+ x

^{2}Â + 3x + 1

**Solution:**

âˆ´Â Remainder is 0, therefore, t

^{2}Â â€“ 3 is a factor of polynomial 2t

^{4}Â + 3t

^{3}Â â€“ 2t

^{2}Â -9t â€“ 12.

âˆ´ Remainder is 0, therefore, x

^{2}Â + 3x + 1 is a factor of polynomial 3x

^{4}Â + 5x

^{3}Â â€“ 7x

^{2}Â + 2x + 2.

âˆ´ Remainder = 2 â‰ 0, therefore, x

^{3}Â â€“ 3x + 1 is not a factor of polynomial x

^{5}Â â€“ 4x

^{3}Â + x

^{2}+ 3x + 1.

**Ex 2.3 Class 10 MathsÂ Question 3.**Â Obtain all other zeroes of 3x

^{4}Â + 6x

^{3}Â â€“ 2x

^{2}Â â€“ 10x â€“ 5, if two of its zeroes areÂ andÂ Â and â€“

**Solution:**

=Â Â x (3x

^{2}â€“ 5).Since bothÂ Â and(3x

^{2}â€“ 5)are the factors, therefore 3x

^{2}Â â€“ 5 is a factor of the given polynomial.

Now, we divide the given polynomial by 3x

^{2}Â â€“ 5.

Hence, the other zeroes of the given polynomial areÂ -1Â andÂ â€“1.

**Ex 2.3 Class 10 MathsÂ Question 4.**On dividing x

^{3Â }â€“ 3x

^{2}Â + x + 2bya polynomial g(x), the quotient and remainder were x â€“ 2 and -2x + 4 respectively. Find g(x).

**Solution:**

x

^{3}Â â€“ 3x

^{2}Â + x + 2Â = g(x) x (x â€“ 2) + (-2x + 4) [By division algorithm]

**Ex 2.3 Class 10 Maths Question 5.**

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and:**(i)** deg p(x) = deg q(x)**(ii)** deg q(x) = deg r(x)**(iii)** deg r(x) = 0**Solution:**

**(i)**p(x) = 2X

^{2}+ 2x + 8,

q(x) = x

^{2}+ x + 4,

g(x) = 2 and r(x) = 0

**(ii)** p(x) = x^{3} + x^{2} + x + 1,

q(x) = x + 1,

g(x) = x^{2} â€“ 1 and r(x) = 2x + 2

**(iii)** p(x) = x^{3} â€“ x^{2} + 2x + 3,

g(x) = x^{2} + 2,

q(x) = x â€“ 1 and r(x) = 5

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