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

Divide the polynomial `3x^4-4x^3-3x-1`by `x-1`

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To divide the polynomial \(3x^4 - 4x^3 - 3x - 1\) by \(x - 1\) using long division, follow these steps: ### Step-by-Step Solution: 1. **Set Up the Division**: Write the polynomial \(3x^4 - 4x^3 - 3x - 1\) under the long division symbol and \(x - 1\) outside. 2. **Divide the Leading Terms**: Divide the leading term of the polynomial \(3x^4\) by the leading term of the divisor \(x\). \[ ...
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Divide the polynomial f(x)=3x^2-x^3-3x+5 by the polynomial g(x)=x-1-x^2 and verify the division algorithm.

Divide the polynomial p(x)=x^4 -3x^2+4x+5 by the polynomial g(x)=x^2-x+1 and find quotient and remainder.

Divide the polynomial u(x)=9x^4-4x^2+4 by the poly-nomial v(x)=3x^2+x-1 . Also, find the quotient and remainder.

Divide the polynomial f(x)=30 x^4+11 x^3-82 x^2-12 x+48 by 3x^2+2x-4 . Also, find the quotient and remainder.

Divide the polynomial g(x) = x^3 - 3x^2 + x + 2 by the polynomial x^2 - 2x + 1 and verify the division algorithm.

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On dividing the polynomial f(x)=x^3-3x^2+x+2 by a polynomial g(x) , the quotient q(x) and remainder r(x) where q(x)=x-2 and r(x)=-2x+4 respectively. Find the polynomial g(x) .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Evaluate 105xx106 without multiplying directly.

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

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

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