Home
Class 9
MATHS
Divide p(x)by g(x), where p(x) = p(x)=x+...

Divide `p(x)`by `g(x)`, where p(x) = `p(x)=x+3x^2-1`and `g(x)=1+x`

Text Solution

AI Generated Solution

To divide the polynomial \( p(x) = x + 3x^2 - 1 \) by \( g(x) = 1 + x \), we will use polynomial long division. Here are the steps: ### Step 1: Arrange the polynomials First, we need to write the polynomials in standard form, which means arranging them in descending order of their degrees. So, we have: - \( p(x) = 3x^2 + x - 1 \) - \( g(x) = x + 1 \) ...
Promotional Banner

Topper's Solved these Questions

  • POLYNOMIALS

    NCERT ENGLISH|Exercise EXERCISE 2.5|16 Videos
  • POLYNOMIALS

    NCERT ENGLISH|Exercise Exercise 2.3|3 Videos
  • POLYNOMIALS

    NCERT ENGLISH|Exercise Exercise 2.2|4 Videos
  • NUMBER SYSTEMS

    NCERT ENGLISH|Exercise EXERCISE 1.4|2 Videos
  • PROBABILITY

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|10 Videos

Similar Questions

Explore conceptually related problems

BY Remainder theorem , find the remainder when p(x) is divided by g(x) (i) p(x) =x^(3)-2x^(2)-4x-1, g(x)=x+1 (ii) p(x) =x^(3)-3x^(2)+4x+50, g(x) =x-3

Divide p(x) by g(x) and find the quotient q(x) and remainder r(x). p(x)=x^(4)+2x^(2)+3, g(x)=x^(2)+1

Divide p(x) by g(x) in each of the following questions and find the quotient q(x) and remainder r(x) : p(x)=x^(3)+6x^(2)-1, " " g(x)=x^(2)+2

Divide p(x) by g(x) in each of the following questions and find the quotient q(x) and remainder r(x) : p(x)=x^(3)-7x^(2)-6x+1, " " g(x)=x-3

Let for a != a_1 != 0 , f(x)=ax^2+bx+c , g(x)=a_1x^2+b_1x+c_1 and p(x) = f(x) - g(x) . If p(x) = 0 only for x = -1 and p(-2) = 2 then the value of p(2) .

In each of the following cases (Q.9-12), find whether g(x) is a factor of p(x) : p(x)=x^(3)-x^(2)+x-1, " " g(x)=x-1

In each of the following cases (Q.9-12), find whether g(x) is a factor of p(x) : p(x)=3x^(3)+5x^(2)-7x-1, " " g(x)=x-1

Divide p(x) by g(x) in each of the following questions and find the quotient q(x) and remainder r(x) : p(x)=x^(3)+3x^(2)+2x+1, " " g(x)=x+2

Divide p(x) by g(x) in each of the following questions and find the quotient q(x) and remainder r(x) : p(x)=3x^(3)-4x^(2)+2x+5, " " g(x)=x+3

In each of the following cases (Q.9-12), find whether g(x) is a factor of p(x) : p(x)=x^(4)+3x^(2)-4, " " g(x)=x+2

NCERT ENGLISH-POLYNOMIALS-SOLVED EXAMPLES
  1. Factorise 8x^3+27 y^3+36 x^2y+54 x y^2.

    Text Solution

    |

  2. Check whether -2\ a n d\ 2 are zeroes of the polynomial x+2.

    Text Solution

    |

  3. Find the value of each of the following polynomials at the indicated ...

    Text Solution

    |

  4. Find the degree of each of the polynomials given below:(i) x^5-x^4+3 ...

    Text Solution

    |

  5. Divide the polynomial 3x^4-4x^3-3x-1by x-1

    Text Solution

    |

  6. Divide p(x)by g(x), where p(x) = p(x)=x+3x^2-1and g(x)=1+x

    Text Solution

    |

  7. Verify whether 2 and 0 are zeroes of the polynomial x^2-2x.

    Text Solution

    |

  8. Find a zero of the polynomial p(x)=2x+1.

    Text Solution

    |

  9. Factorise: (i) 49 a^2+70 a b+25 b^2 (ii) (25)/4x^2-(y^2)/9

    Text Solution

    |

  10. Write (3a\ +\ 4b\ +\ 5c)^2in expanded form.

    Text Solution

    |

  11. Check whether the polynomial q(t)=4t^3+4t^2-t-1is a multiple of 2t+1

    Text Solution

    |

  12. Examine whether x+2 is a factor of x^3+3x^2+5x+6 and of 2x+4.

    Text Solution

    |

  13. Find the value of k, if x-1is a factor of 4x^3+3x^2-4x+k.

    Text Solution

    |

  14. Factorise 6x^2+17 x+5 by splitting the middle term, and by using the ...

    Text Solution

    |

  15. Factorise y^2-5y+6 by using the Factor Theorem.

    Text Solution

    |

  16. Factorise x^2-23 x^2+142 x-120 .

    Text Solution

    |

  17. Find the following products using appropriate identities:(i)\ (x+3)\ ...

    Text Solution

    |

  18. Evaluate 105xx106 without multiplying directly.

    Text Solution

    |

  19. Evaluate each of the following using suitable identities:(i) (104)^3 ...

    Text Solution

    |

  20. Find the remainder obtained on dividing p(x)=x^3+1 by x+1

    Text Solution

    |