Answer :

Final answer:

The student's question pertains to the division of a polynomial by a binomial, requiring long division for polynomials. The question contained examples of dividing in scientific notation, which employs different rules by dividing coefficients and subtracting exponents. However, the question itself seemed to have typos, and the presented examples do not directly apply to the polynomial division in question.

Explanation:

Division of a Polynomial by a Binomial

To divide the polynomial 10x^3 - 19x^2 + 21x - 14 by the binomial 5x^2 - 2x, we follow the long division algorithm for polynomials. We would divide the leading term of the polynomial by the leading term of the binomial, subtract the result from the polynomial, and then repeat the process with the resulting polynomial until we have a remainder that is of a lower degree than the binomial, or until there is no remainder.

The question, however, seems to contain typos or syntax errors as such division, while possible, won't yield any of the provided scientific notation examples directly. The summary provides different instances of scientific notation division, which involves dividing the coefficients (digit terms) and subtracting the exponents of the powers of ten when in scientific notation. This is different from the polynomial division mentioned in the question.

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