Home
Class 9
MATHS
f(x)=3x^4+17 x^3+9x^2-7x-10 ;g(x)=x+5...

`f(x)=3x^4+17 x^3+9x^2-7x-10 ;g(x)=x+5`

Text Solution

Verified by Experts

1409703 `f(x)=3x^4+17x^3+9x^2-7x-10`
`g(x)=x+5`
Using the factor theorem, `g(x)` is a factor of polynomial `f(x)`
`g(x)=x+5=0`
`x=-5`
Then,
`f(-5)=3(-5)^4+17(-5)^3+9(-5)^2-7(5)-10`
`=>3(625)+17(-125)+225+35-10`
`=>1875-2125+250=0`
`therefore` The `g(x)` is the factor of polynomial `f(x)`.
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

f(x)=x^(3)+4x^(2)-3x+10,g(x)=x+4

check whether g(x) is a factor of f(x) or not f(x)= x^5+3x^4−x^3−3x^2+5x+15 , 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)=3x^(3)+5x^(2)-7x-1, " " g(x)=x-1

Find the intervals in which the following function are increasing or decreasing. f(x)=10-6x-2x^2 f(x)=x^2+2x-5 f(x)=6-9x-x^2 f(x)=2x^3-12 x^2+18 x+15 f(x)=5+36 x+3x^2-2x^3 f(x)=8+36 x+3x^2-2x^3 f(x)=5x^3-15 x^2-120 x+3 f(x)=x^3-6x^2-36 x+2 f(x)=2x^3-15 x^2+36 x+1 f(x)=2x^3+9x^2+20 f(x)=2x^3-9x^2+12 x-5 f(x)=6+12 x+3x^2-2x^3 f(x)=2x^3-24 x+107 f(x)=-2x^3-9x^2-12 x+1 f(x)=(x-1)(x-2)^2 f(x)=x^3-12 x^2+36 x+17 f(x)=2x^3-24+7 f(x)=3/(10)x^4-4/5x^3-3x^2+(36)/5x+11 f(x)=x^4-4x f(x)=(x^4)/4+2/3x^3-5/2x^2-6x+7 f(x)=x^4-4x^3+4x^2+15 f(x)=5x^(3/2)-3x^(5/2),x >0 f(x)==x^8+6x^2 f(x)==x^3-6x^2+9x+15 f(x)={x(x-2)}^2 f(x)=3x^4-4x^3-12 x^2+5 f(x)=3/2x^4-4x^3-45 x^2+51 f(x)=log(2+x)-(2x)/(2+x),xR

f(x)=2x^(3)-9x^(2)+x+12,g(x)=3-2x

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x)=10x^(4)+17x^(3)-62x^(2)+30x-3 by g(x)=2x^(2)+7x+1

f(x)=9x^(3)-3x^(2)+x-5,g(x)=x-(2)/(3)

" 2" f(x)=4x^(4)-3x^(3)-2x^(2)+x-7,g(x)=x-1

Verify the division algorithm for the polynomials p(x)=2x^(4)-6x^(3)+2x^(2)-x+2andg(x)=x+2 . p(x)=2x^(3)-7x^(2)+9x-13,g(x)=x-3 .

If f (x) = (3x + 4)/( 5x -7), g (x) = (7x +4)/(5x -3) then f [g(x)]=

RD SHARMA-FACTORIZATION OF POLYNOMIAL-All Questions
  1. What must be added to x^4+2x^3-2x^2+x-1 so that the result is exactly ...

    Text Solution

    |

  2. f(x)=x^3-6x^2+11 x-6;g(x)=x-3

    Text Solution

    |

  3. f(x)=3x^4+17 x^3+9x^2-7x-10 ;g(x)=x+5

    Text Solution

    |

  4. check whether g(x) is a factor of f(x) or not f(x)=x^5+3x^4−x^3−3x^2+...

    Text Solution

    |

  5. f(x)=x^3-6x^2-19 x+84 ,\ g(x)=x-7

    Text Solution

    |

  6. f(x)=3x^3+x^2-20 x+12 ,\ g(x)=3x-2

    Text Solution

    |

  7. Using the remainder theorem, find out whether g(x) is factor of f(x) o...

    Text Solution

    |

  8. f(x)=x^3-6x^2+11 x-6,\ g(x)=x^2-3x+2

    Text Solution

    |

  9. Show that (x-2),(x+3) and (x-4) are factors of x^3-3x^2-10x+24.

    Text Solution

    |

  10. Show that (x+4),\ (x-3)a n d\ (x-7) are factors of x^3-6x^2-19 x+84

    Text Solution

    |

  11. For what value of a is (x-5) a factor of x^3-3x^2+a x-10 ?

    Text Solution

    |

  12. Find the value of a such that (x-4) is a factor of 5x^3-7x^2-a x-28

    Text Solution

    |

  13. Find the value of a , if x+2 is a factor of 4x^4+2x^3-3x^2+8x+5a

    Text Solution

    |

  14. Find the value of k if x-3 is a factor of k^2x^3-k x^2+3k x-k

    Text Solution

    |

  15. Find the values of a and b, if x^2-4 is a factor of ax^4+2x^3-3x^2+bx-...

    Text Solution

    |

  16. Find alpha\ a n d\ beta , if x+1\ a n d\ x+2 are factors of x^3+3x^2-2...

    Text Solution

    |

  17. Find the values of p\ a n d\ q so that x^4+p x^3+2x^2-3x+q is divisibl...

    Text Solution

    |

  18. Find the values of a\ a n d\ b so that (x+1)a n d\ (x-1) are factors o...

    Text Solution

    |

  19. If x^3+a x^2-b x+10 is divisible by x^2-3x+2, find the values of a and...

    Text Solution

    |

  20. if (x+1) and (x-1) are factors of p(x)=ax^3+x^2-2x+b find the values o...

    Text Solution

    |