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X-1/x^3-1Division by long division method |
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Answer» Answer: Enter a problem... Algebra Examples Popular Problems Algebra Divide Using Long Polynomial Division (x^3-1)÷(x-1) ( x 3 − 1 ) ÷ ( x − 1 ) Set up the POLYNOMIALS to be divided. If there is not a term for every exponent, insert one with a value of 0 . x - 1 x 3 + 0 x 2 + 0 x - 1 Divide the highest order term in the dividend x 3 by the highest order term in divisor x . x 2 x - 1 x 3 + 0 x 2 + 0 x - 1 Multiply the new quotient term by the divisor. x 2 x - 1 x 3 + 0 x 2 + 0 x - 1 + x 3 - x 2 The expression needs to be subtracted from the dividend, so change all the signs in x 3 − x 2 x 2 x - 1 x 3 + 0 x 2 + 0 x - 1 - x 3 + x 2 After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend. x 2 x - 1 x 3 + 0 x 2 + 0 x - 1 - x 3 + x 2 + x 2 Pull the NEXT terms from the original dividend down into the current dividend. x 2 x - 1 x 3 + 0 x 2 + 0 x - 1 - x 3 + x 2 + x 2 + 0 x Divide the highest order term in the dividend x 2 by the highest order term in divisor x . x 2 + x x - 1 x 3 + 0 x 2 + 0 x - 1 - x 3 + x 2 + x 2 + 0 x Multiply the new quotient term by the divisor. x 2 + x x - 1 x 3 + 0 x 2 + 0 x - 1 - x 3 + x 2 + x 2 + 0 x + x 2 - x The expression needs to be subtracted from the dividend, so change all the signs in x 2 − x x 2 + x x - 1 x 3 + 0 x 2 + 0 x - 1 - x 3 + x 2 + x 2 + 0 x - x 2 + x After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend. x 2 + x x - 1 x 3 + 0 x 2 + 0 x - 1 - x 3 + x 2 + x 2 + 0 x - x 2 + x + x Pull the next terms from the original dividend down into the current dividend. x 2 + x x - 1 x 3 + 0 x 2 + 0 x - 1 - x 3 + x 2 + x 2 + 0 x - x 2 + x + x - 1 Divide the highest order term in the dividend x by the highest order term in divisor x . x 2 + x + 1 x - 1 x 3 + 0 x 2 + 0 x - 1 - x 3 + x 2 + x 2 + 0 x - x 2 + x + x - 1 Multiply the new quotient term by the divisor. x 2 + x + 1 x - 1 x 3 + 0 x 2 + 0 x - 1 - x 3 + x 2 + x 2 + 0 x - x 2 + x + x - 1 + x - 1 The expression needs to be subtracted from the dividend, so change all the signs in x − 1 x 2 + x + 1 x - 1 x 3 + 0 x 2 + 0 x - 1 - x 3 + x 2 + x 2 + 0 x - x 2 + x + x - 1 - x + 1 After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend. x 2 + x + 1 x - 1 x 3 + 0 x 2 + 0 x - 1 - x 3 + x 2 + x 2 + 0 x - x 2 + x + x - 1 - x + 1 0 Since the REMANDER is 0 , the final answer is the quotient. x 2 + x + 1 |
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