Answer: (2x^2 + 3x - 4)/(x + 2) is 2x - 1 with a remainder of -2
Explanation:
To simplify the algebraic expression (2x^2 + 3x - 4)/(x + 2), we can use the method of polynomial long division. Here are the steps:
1. Divide the highest degree term of the numerator (2x^2) by the highest degree term of the denominator (x). This gives us 2x.
2. Multiply the entire denominator (x + 2) by the quotient obtained in step 1 (2x). This gives us 2x^2 + 4x.
3. Subtract the result from step 2 from the numerator (2x^2 + 3x - 4). This gives us (2x^2 + 3x - 4) - (2x^2 + 4x) = -x - 4.
4. Bring down the next term from the numerator (-x - 4) and repeat steps 1 to 3.
5. Divide the new highest degree term (-x) by the highest degree term of the denominator (x). This gives us -1.
6. Multiply the entire denominator (x + 2) by the quotient obtained in step 5 (-1). This gives us -x - 2.
7. Subtract the result from step 6 from the numerator (-x - 4). This gives us (-x - 4) - (-x - 2) = -2.
8. The result of the division is the quotient (2x - 1) and the remainder (-2).
Therefore, the simplified form of the expression (2x^2 + 3x - 4)/(x + 2) is 2x - 1 with a remainder of -2.