Answer :
Final answer:
The answer to the synthetic division of the polynomial by the binomial is 10x⁴ + 17x³ + 55x² + 199x + 790 + 3141/(x−4).
Explanation:
To perform synthetic division of the polynomial (10x⁵−23x⁴−13x³−21x²−6x−19) by the binomial (x−4), we should first organize the terms in descending order of their degrees. Next, we perform the synthetic division as follows:
4 | 10 -23 -13 -21 -6 -19
| +40 68 220 796 3160
-----------------------------
= 10 17 55 199 790 3141
Thus, the result in fraction form of the division is 10x⁴ + 17x³ + 55x² + 199x + 790 + 3141/x−4.
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