answer:
To divide the expression (2x^3 + 4x^2 - 5) by (x + 3), we can use polynomial long division. Here's how:
1. Divide the first term of the numerator (2x^3) by the first term of the denominator (x). The result is 2x^2.
2. Multiply the entire denominator (x + 3) by the result from step 1 (2x^2). The result is 2x^3 + 6x^2.
3. Subtract the result from step 2 from the numerator (2x^3 + 4x^2 - 5) to get the remainder. The remainder is -2x^2 - 5.
4. Bring down the next term from the numerator (-2x^2) and divide it by the first term of the denominator (x). The result is -2x.
5. Multiply the entire denominator (x + 3) by the result from step 4 (-2x). The result is -2x^2 - 6x.
6. Subtract the result from step 5 from the remainder (-2x^2 - 5) to get the new remainder. The new remainder is x - 5.
7. Bring down the next term from the numerator (x) and divide it by the first term of the denominator (x). The result is 1.
8. Multiply the entire denominator (x + 3) by the result from step 7 (1). The result is x + 3.
9. Subtract the result from step 8 from the new remainder (x - 5) to get the final remainder. The final remainder is -8.
Therefore, the division of (2x^3 + 4x^2 - 5) by (x + 3) is equal to 2x^2 - 2x + 1, with a remainder of -8.
We can write this as the quotient (2x^2 - 2x + 1) plus the remainder (-8), all divided by the original denominator (x + 3).
So the final expression is: (2x^2 - 2x + 1 - 8)/(x + 3), which simplifies to (2x^2 - 2x - 7)/(x + 3).
i did it !!