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Algebraic Expressions

Simplify the algebraic expression: (2x^2 + 3x - 4)/(x + 2).

A) 2x - 2
B) 2x + 2
C) 3x - 4
D) 3x + 4

User Ineu
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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.

User Keemahs
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