How do you long divide #(x^3 + x^2 - x - 1) div(x - 1)#?
1 Answer
Explanation:
Long dividing polynomials is similar to long dividing integers...
Write the dividend under the bar and the divisor to the left.
Choose the first term of the quotient so that when multiplied by the divisor it matches the leading term of the dividend. In our case, we write
Write this product under the dividend and subtract it to give a remainder
Choose the next term of the quotient so that when multiplied by the divisor it matches the leading term in the remainder. In our case, we write
Write this product under the remainder and subtract it to give a remainder
Choose the final term of the quotient so that when multiplied by the divisor it matches the leading term in the remainder. In our case, we write
Write this product under the remainder and subtract it. No remainder is left and there are no more terms in the divisor to bring down, so we're done.
In this case the division was exact. In general, you may be left with a remainder at the end.