(b) Sally set up the problem and is stuck doing the division properly. Help Sally find her error [ x-2 sqrt(x^3)+0 x^(2-9 x+10) -x^3+2 x^2-9 x (-2 x^2+4 x)/(0-5 x+10) (5 x-10)/(0) ] (A) Sally's initial setup is wrong b / c there is a coefficient of zero in the cubic. B Sally's second step is wrong b / c-2 multiplied by 2 x is -4 x (C) In the final step, Sally should have multiplied by -5 instead of using 5 (D) All of Sally's work is correct.

## Step 1: Analyze Sally's Work<br />### We need to carefully check each step of Sally's polynomial division to identify any errors.<br /><br />## Step 2: Verify Initial Setup<br />### The initial setup provided by Sally is correct. She correctly sets up the dividend \( x^3 + 0x^2 - 9x + 10 \) and the divisor \( x - 2 \).<br /><br />## Step 3: Check First Division Step<br />### Sally divides \( x^3 \) by \( x \) to get \( x^2 \), which is correct. She then multiplies \( x^2 \) by \( x - 2 \) to get \( x^3 - 2x^2 \). Subtracting this from \( x^3 + 0x^2 \) results in \( 2x^2 \), which is also correct.<br /><br />## Step 4: Check Second Division Step<br />### Sally brings down the next term, resulting in \( 2x^2 - 9x \). She divides \( 2x^2 \) by \( x \) to get \( 2x \), which is correct. However, when she multiplies \( 2x \) by \( x - 2 \), she should get \( 2x^2 - 4x \). Subtracting \( 2x^2 - 4x \) from \( 2x^2 - 9x \) should result in \( -5x \). This indicates that her second step is correct.<br /><br />## Step 5: Check Third Division Step<br />### Sally brings down the last term, resulting in \( -5x + 10 \). She divides \( -5x \) by \( x \) to get \( -5 \), which is correct. She then multiplies \( -5 \) by \( x - 2 \) to get \( -5x + 10 \). Subtracting \( -5x + 10 \) from \( -5x + 10 \) results in \( 0 \), which is correct.<br /><br />## Step 6: Identify Error<br />### Upon reviewing all steps, it appears that Sally's work is correct. There are no errors in her polynomial division process.