Answer:
Explanation:
To divide the polynomial (x^3+2x^2-20x-33) by (x+5), we can use long division. Here are the steps:
1. Begin by dividing the first term of the dividend (x^3) by the first term of the divisor (x). The result is x^2. Write this above the division symbol.
2. Multiply the entire divisor (x+5) by the result from step 1 (x^2). This gives you x^3+5x^2.
3. Subtract this result (x^3+5x^2) from the original dividend (x^3+2x^2-20x-33). This will cancel out the x^3 term, leaving you with -3x^2-20x-33.
4. Bring down the next term from the dividend, which is -20x.
5. Repeat steps 1-3 with the new expression (-3x^2-20x-33) and the divisor (x+5).
6. Dividing -3x^2 by x gives you -3x. Write this above the division symbol.
7. Multiply the entire divisor (x+5) by -3x. This gives you -3x^2-15x.
8. Subtract this result (-3x^2-15x) from the expression -3x^2-20x-33. This will cancel out the -3x^2 term, leaving you with -5x-33.
9. Bring down the next term from the dividend, which is -33.
10. Repeat steps 1-3 with the new expression (-5x-33) and the divisor (x+5).
11. Dividing -5x by x gives you -5. Write this above the division symbol.
12. Multiply the entire divisor (x+5) by -5. This gives you -5x-25.
13. Subtract this result (-5x-25) from the expression -5x-33. This will cancel out the -5x term, leaving you with -8.
14. There are no more terms to bring down from the dividend.
15. The final result is x^2-3x-5 with a remainder of -8.
Therefore, (x^3+2x^2-20x-33) divided by (x+5) is equal to x^2-3x-5 with a remainder of -8.