Final Answer:
The expression (x³ + 2x² + 3x - 4)/(x - 1) can be expressed in mixed number form as x² + 3x + 7 with a remainder of 3/(x - 1).
Step-by-step explanation:
To obtain the mixed number form, we perform long division on the given polynomial expression. Starting with x³ + 2x² + 3x - 4 divided by (x - 1), we divide x into x³ to get x².
Then, we multiply (x - 1) by x² to get x³ - x². Subtracting this from the original expression leaves us with 3x² + 4x - 4. We continue the process by dividing x into 3x², resulting in 3x. Multiplying (x - 1) by 3x gives 3x² - 3x, and subtracting this from the remaining expression leaves 7x - 4. We proceed by dividing x into 7x, obtaining 7. Multiplying (x - 1) by 7 gives 7x - 7, and subtracting this from the remaining expression leaves a remainder of 3.
Expressing the result in mixed number form, we have x² + 3x + 7 with a remainder of 3/(x - 1). This representation provides a clear and concise way of expressing the polynomial expression in terms of its quotient and remainder.