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Find the values of a and b so that the p...

Find the values of a and b so that the polynomial `x^3+10 x^2+ax+b` is exactly divisible by x-1 as well as x-2.

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RD SHARMA ENGLISH-FACTORIZATION OF POLYNOMIAL-All Questions
  1. If a x^3+b x^2+x-6 has x+2 as a factor and leaves a remainder 4 when d...

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

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

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

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

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

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

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

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  9. If the polynomials a x^3+3x^2-13 and 2x^3-5x+a , when divided by (x-2)...

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  10. Show that (x-1) is a factor of x^(10)-1 and also of x^(11)-1.

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  11. Identify polynomials in the following: (i) f(x)=4x^3-x^2-3x+7 (ii) g(...

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  12. Show that x=1 is a root of the polynomial 2x^3-3x^2+7x-6

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  13. If x=4/3 is a root of the polynomial f(x)=6x^3-11 x^2+k x-20 , find th...

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  14. If x=2 and x=0 are roots of the polynomial f(x)=2x^3-5x^2+a x+bdot Fin...

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  15. Which of the following expressions are polynomials in one variable a...

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  16. Write the degrees of each of the following polynomials: (i) 7x^3+4x^...

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  17. Classify the following polynomials as polynomials in one-variable, ...

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  18. Using factor theorem, factorize the polynomial x^3-6x^2+11 x-6 .

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  19. Find the rational roots of the polynomial 2x^3+3x^2-11 x-6

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  20. If x=0 and x=-1 are the roots of the polynomial f(x)=2x^3-3x^2+a x+b ,...

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