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(x^(3)+7x^(2)+2)÷(x-1)

77. (x3+7x2+2)÷(x−1) \left(x^{3}+7 x^{2}+2\right) \div(x-1)

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Q. 77. (x3+7x2+2)÷(x−1) \left(x^{3}+7 x^{2}+2\right) \div(x-1)
  1. Set up division: Step 11: Set up the division.\newlineWe need to divide x3+7x2+0x+2x^3 + 7x^2 + 0x + 2 by x−1x - 1.
  2. Perform first division: Step 22: Perform the first division.\newlineDivide the highest degree term of the dividend by the highest degree term of the divisor.\newlinex3x=x2\frac{x^3}{x} = x^2.\newlineMultiply x2x^2 by x−1x - 1 and subtract from the original polynomial.\newlinex3+7x2−(x3−x2)=8x2x^3 + 7x^2 - (x^3 - x^2) = 8x^2.
  3. Perform second division: Step 33: Perform the second division.\newlineDivide 8x28x^2 by xx.\newline8x2x=8x\frac{8x^2}{x} = 8x.\newlineMultiply 8x8x by x−1x - 1 and subtract.\newline8x2+0x−(8x2−8x)=8x8x^2 + 0x - (8x^2 - 8x) = 8x.
  4. Perform third division: Step 44: Perform the third division.\newlineDivide 8x8x by xx.\newline8xx=8\frac{8x}{x} = 8.\newlineMultiply 88 by x−1x - 1 and subtract.\newline8x+2−(8x−8)=108x + 2 - (8x - 8) = 10.
  5. Write final answer: Step 55: Write the final answer.\newlineThe quotient is x2+8x+8x^2 + 8x + 8 with a remainder of 1010.\newlineThus, (x3+7x2+2)÷(x−1)=x2+8x+8+10x−1(x^3 + 7x^2 + 2) ÷ (x - 1) = x^2 + 8x + 8 + \frac{10}{x-1}.

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