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If f(x)=x^4-2x^3+3x^2-a x-b when divided...

If `f(x)=x^4-2x^3+3x^2-a x-b` when divided by `x-1` , the remainder is `6,` then find the value of `a+b`

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when divided by, `x-1=0,x=1`
`f(1)=(1)^4-2(1)^3+3(1)^2-a(1)-b`
`2-a-b=6`
`-(a+b)=4`
`a+b=-4`
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RD SHARMA-FACTORIZATION OF POLYNOMIAL-All Questions
  1. Find the remainder when x^3+4x^2+4x-3 is divided by x

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  2. If x+1 is a factor of x^3+a , then write the value of a

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  3. If f(x)=x^4-2x^3+3x^2-a x-b when divided by x-1 , the remainder is 6, ...

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  4. If x-2 is a factor of x^2+3a x-2a, then a= 2 (b) -2 (c) 1 (d) -1

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  5. If x^3+6x^2+4x+k , is exactly divisible by (x+2), then the value of k ...

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  6. If x-a is a factor of x^3-3x^2a+2a^2x+b , then the value of b is 0 (b)...

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  7. If x^(140)+2x^(151)+k is divisible by x+1 , then the value of k is=? ...

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  8. If x+2 and x-1 are the factors of x^3+10 x^2+m x+n, then the values of...

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  9. Let f(x) be a polynomial such that f(-1/2)=0, then a factor of f(x) ...

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  10. When x^3-2x^2+a x-b is divided by x^2-2x-3, the remainder is x-6. The ...

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  11. One factor of x^4+x^2-20 is x^2+5. The other factor is x^2-4\ (b) ...

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  12. If (x-1) is a factor of polynomial f(x) but not of g(x) , then it mu...

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  13. (x+1) is a factor of x^n+1 only if  (a)n is an odd integer   (b) n i...

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  14. If x+2\ is a factor of x^2+m x+14 , then m= (a)7 (b) 2 (c) 9 (d) ...

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  15. If x-3 is a factor of x^2-a x-15, then a=

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  16. If x^2+x+1 is a factor of the polynomial 3x^3+8x^2+8x+3+5k , then th...

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  17. If (3x-1)^7=a7x^7+a6x^6+a5x^5+....+a1x+a0 then the value of a7 + a6. ....

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  18. If x^(51)+51 is divided by x+1 , the remainder is 0 (b) 1 (c) 49 (...

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  19. If x+1 is a factor of the polynomial 2x^2+k x , then k= -2 (b) -3 ...

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  20. If x+a is a factor of x^4-a^2x^2+3x-6a , then a= 0 (b) -1 (c) 1 (d) ...

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