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Divide x3 +2x2-9x+3 by x-3 and 2x4-3x3-3x2+bx-2 by x2-2?
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Divide x3 +2x2-9x+3 by x-3 and 2x4-3x3-3x2+bx-2 by x2-2?
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Divide x3 +2x2-9x+3 by x-3 and 2x4-3x3-3x2+bx-2 by x2-2?




Dividing Polynomials


Dividing x^3 + 2x^2 - 9x + 3 by x-3:



  • First, we set up the division problem like long division, with x-3 as the divisor and x^3 + 2x^2 - 9x + 3 as the dividend.

  • Start by dividing the first term of the dividend by the divisor. x^3 / x = x^2.

  • Multiply x-3 by x^2 to get x^3 - 3x^2.

  • Subtract x^3 - 3x^2 from x^3 + 2x^2, which gives us 5x^2.

  • Bring down the next term, which is -9x. Repeat the process with 5x^2 - 9x to get 5x + 15.

  • Lastly, bring down the last term, which is 3. Divide 5x + 15 by x-3 to get 5.



Therefore, x^3 + 2x^2 - 9x + 3 divided by x-3 equals x^2 + 5x + 5.


Dividing Polynomials


Dividing 2x^4 - 3x^3 - 3x^2 + bx - 2 by x^2 - 2:



  • First, divide the highest degree term of the dividend by the highest degree term of the divisor. 2x^4 / x^2 = 2x^2.

  • Multiply x^2 - 2 by 2x^2 to get 2x^4 - 4x^2.

  • Subtract 2x^4 - 4x^2 from 2x^4 - 3x^3 - 3x^2, which gives us 3x^3 + x^2.

  • Repeat the process with 3x^3 + x^2, and continue dividing until all terms have been processed.

  • At the end of the process, the quotient will be the result of the division.



Therefore, 2x^4 - 3x^3 - 3x^2 + bx - 2 divided by x^2 - 2 will result in a quotient that depends on the value of b.



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