Answer :
Final answer:
The quotient of (5x⁴ - 3x² - 4x + 6) divided by (x - 7) is 5x³ - 35x² + 226x - 1579 and the remainder is 11153.
Explanation:
To answer this question, we divide the polynomial (5x⁴ - 3x² - 4x + 6) by the monomial (x - 7) using the polynomial division method. Starting from the highest degree term, we divide the term from the polynomial by the term from the monomial. For instance, we first divide 5x⁴ by x, resulting in 5x³.
We then multiply 5x³ with (x - 7), which yields (5x⁴ - 35x³). Then, we subtract this result from the first two terms of the polynomial and continue the process. After performing these steps repeatedly for each term of the polynomial, we arrive at the answer.
Therefore, the quotient of (5x⁴ - 3x² - 4x + 6) divided by (x - 7) is 5x³ - 35x² + 226x - 1579 and the remainder is 11153. So the correct answer is A. Quotient: 5x³ - 35x² + 226x - 1579, Remainder: 11153.
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