To divide the polynomial 2x² + 17x + 35 by x + 5, we can use polynomial long division.
1. First, set up the division: Write 2x² + 17x + 35 under the long division symbol and x + 5 outside.
2. Next, divide the leading term of the dividend (2x²) by the leading term of the divisor (x) to find the first term of the quotient: 2x.
3. Now, multiply the entire divisor (x + 5) by 2x, giving you 2x² + 10x. Write this result beneath the dividend.
4. Subtract (2x² + 10x) from (2x² + 17x + 35). To do this, invert the signs of the terms you just wrote and add:
- 2x² – 2x² = 0
- 17x – 10x = 7x
- 35 remains unchanged.
This results in 7x + 35.
5. Next, repeat the process. Divide the leading term of the new expression (7x) by the leading term of the divisor (x) to get 7.
6. Multiply the divisor by 7: 7(x + 5) = 7x + 35. Write this below (7x + 35).
7. Subtract (7x + 35) from (7x + 35):
- 7x – 7x = 0
- 35 – 35 = 0
This results in a remainder of 0.
Thus, the complete division of 2x² + 17x + 35 by x + 5 gives us:
2x + 7 with a remainder of 0.