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. It is a way of dividing polynomials by binomials wherein you only write the numerical coefficients and constants in the solution.

Question

It is a way of dividing polynomials by binomials wherein you only write the numerical coefficients and constants in the solution.

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Solution

The method you're referring to is known as Synthetic Division. Here are the steps to perform synthetic division:

  1. Write down the coefficients of the dividend (the polynomial you're dividing into) and the zero of the divisor (the value that makes the binomial equal to zero).

  2. Bring down the leading coefficient (the first number) to the bottom row.

  3. Multiply the value you just wrote down by the zero of the divisor, and write the result under the next coefficient.

  4. Add the numbers in this new column together and write the result at the bottom.

  5. Repeat steps 3 and 4 until you've worked through all the coefficients.

  6. The numbers on the bottom row represent the coefficients of the quotient, and the last number is the remainder. If the remainder is zero, then the divisor is a factor of the dividend.

Remember, synthetic division only works when dividing by binomials of the form x - k.

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