Final Answer:
The result of dividing the polynomial expression (2x³ + 5x² - 8x + 4) by the binomial (x - 2) is 2x² + 9x - 14.
Step-by-step explanation:
To perform polynomial division, we use the long division method. In this case, we divide the highest degree term of the numerator, 2x³ , by the highest degree term of the denominator, x. The result is 2x², which is then multiplied by the entire denominator (x - 2). The product, 2x³ - 4x², is subtracted from the numerator, and the process is repeated.
The second step involves bringing down the next term from the numerator, which is 5x². Now, we divide 5x² by x, resulting in +5x. This term is multiplied by the denominator, giving us 5x² - 10x. Subtracting this from the remaining part of the numerator yields a remainder of +2x.
Lastly, we bring down the next term, -8x, and divide it by x, obtaining -8. This is multiplied by the denominator, resulting in -8x + 16. Subtracting this from the remainder leaves us with -14.
The final answer is the quotient obtained during this process: 2x² + 9x - 14. This represents the result of dividing the given polynomial expression by the specified binomial.