Final answer:
After multiplying d by (s-2) and setting s = 1 to isolate d, the equation simplifies to d = x² - 4x + 9, and after adding 2d, the result is d = x² - 4x + 11, which matches option d.
Step-by-step explanation:
The student has given the equation: d(s-2)=-x²+4x-9. To express this in simplest form and in descending order of degree, we need to distribute and simplify.
Step by step, this is done as follows:
- Multiply d by each term inside the parentheses: d × s gives ds, and d × -2 gives -2d. So the left side of the equation becomes ds - 2d.
- Set this equal to the right side of the equation, which is -x² + 4x - 9.
- We will then have ds - 2d = -x² + 4x - 9.
- To solve for d, we first isolate ds on the left side. For s = 1, the equation becomes d - 2d = -x² + 4x - 9.
- Combine the d terms on the left to get -d.
- Divide each term by -1 to solve for d: d = x² - 4x + 9.
- Add 2d to each side to make up for the initial distribution which gives us d = x² - 4x + 9 + 2.
- Simplify the constants to get d = x² - 4x + 11.
Hence, the correct expression in simplest form in descending order of degree is d = x² - 4x + 11 (Answer d).