Home
Class 9
MATHS
Without actual division prove that 2x^4-...

Without actual division prove that `2x^4- 6x^3 +3x^2+3x-2` is exactly divisible by `x^2- 3x +2` is

Text Solution

Verified by Experts

`P(x)=2x^4−5x^3+2x^2−x+2` and
`x^2−3x+2=(x−1)(x−2)`
Let `x^2−3x+2` is the factor of `P(x)`
Then, `x^2−3x+2=0`
`⇒(x−1)(x−2)=0`
`⇒x=1` and `2`
For `x=1`
`P(1)=0`
For `x=2`
`P(2)=0`
`∵P(1)=P(2)=0`
`∴P(x)` is divisible by `x^2−3x+2`
Promotional Banner

Topper's Solved these Questions

  • FACTORIZATION OF ALGEBRAIC EXPRESSIONS

    RD SHARMA|Exercise All Questions|226 Videos

  • GRAPHICAL REPRESENTATION OF STATISTICAL DATA

    RD SHARMA|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

Without actual division prove that 2x^(4)-6x^(3)+3x^(2)+3x-2 is exactly division by x^(2)-3x+2

Without actual division,prove that (2x^(4)-6x^(3)+3x+3x-2) is exactly divisible by (x^(2)-3x+2)

Without actual division,prove that 2x^(4)-5x^(3)+2x^(2)-x+2 is exactly divisible by x^(2)-3x+2

Without actual division,prove that x^(4)+2x^(3)-2x^(2)+2x-3 is exactly divisible by x^(2)+2x-3.

Without actual division, prove that 2x^(4)-5x^(3)+2x^(2)-x+2 is divisible by x^(2)-3x+2 .

Without actual division , prove that 2x^(4)-5x^(3)+2x^(2)-x+2 is divisible by x^(2)-3x+2 .

Without actual division,show that x^(3)-3x^(2)-13x+15 is exactly divisible by (x^(2)+2x-3)

Without actual division , prove that (2x^(4)+3x^(3)-12x^(2)-7x+6) is exactly divisible by (x^(2)+x-6) .

4x^(3) + 12x^(2) - x - 3 is divisible by

Prove that 2x^(4)-9x^(3)+21x^(2)-26x+12 is completely divisible by 2x-3.

RD SHARMA-FACTORIZATION OF POLYNOMIAL-All Questions
  1. Show that (x-1) is a factor of x^(10)-1 and also of x^(11)-1.

    Text Solution

    |

  2. Show that x+1 and 2x-3 are factors of 2x^3-9x^2+x+12

    Text Solution

    |

  3. Without actual division prove that 2x^4- 6x^3 +3x^2+3x-2 is exactly di...

    Text Solution

    |

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

    Text Solution

    |

  5. Find the value of k , if x+3 is a factor of 3x^2+k x+6.

    Text Solution

    |

  6. Determine the value of a for which the polynomial 2x^4-a x^3+4x^2+2x+1...

    Text Solution

    |

  7. Find the value of a and b so that the polynomial x^3-a x^2-13 x+b has ...

    Text Solution

    |

  8. Find the values of a and b so that the polynomial x^3+10 x^2+a x+b is ...

    Text Solution

    |

  9. For what values of a is 2x^3+a x^2+11 x+a+3 exactly divisible by (2x-1...

    Text Solution

    |

  10. If a x^3+b x^2+x-6 has x+2 as a factor and leaves a remainder 4 when d...

    Text Solution

    |

  11. If both x-2 and x-1/2 are factors of p x^2+5x+r , show that p=rdot

    Text Solution

    |

  12. If x^2-1 is a factor of a x^4+b x^3+c x^2+dx+e , show that a+c+e=b+d

    Text Solution

    |

  13. Without actual division, prove that 2x^4-5x^3+2x^2-x+2 is exactly divi...

    Text Solution

    |

  14. Without actual division, prove that x^4+2x^3-2x^2+2x-3 is exactly divi...

    Text Solution

    |

  15. In each of the following polynomials, find the value of a if x+a is ...

    Text Solution

    |

  16. In each of the following polynomials, find the value of a if x+a is ...

    Text Solution

    |

  17. Use factor theorem to verify that x+a is a factor of x^n+a^n for any o...

    Text Solution

    |

  18. If f(x)=x^4-2x^3+3x^2-a x+b is a polynomial such that when it is divid...

    Text Solution

    |

  19. What must be subtracted from 4x^4-2x^3-6x^2+x-5 so that the result is...

    Text Solution

    |

  20. What must be added to x^4+2x^3-2x^2+x-1 so that the result is exactly ...

    Text Solution

    |