Question

Fill in the missing values below one at a time to find the quotient when minus, 8, x, cubed, plus, 26, x, squared, minus, 25−8x
3
+26x
2
−25 is divided by minus, 4, x, plus, 5−4x+5.
The table below, forming a box method diagram, contains an input box in one of the cells. A "try" button follows the diagram. After pressing the "try" button, if your answer is correct, it will be placed on the diagram and a new input box will appear in another cell. This process will continue until all boxes on the diagram are filled and then the final answer area will appear.
minus, 4, x−4x minus, 8, x, cubed−8x
3

plus, 5+5

Answer 1

Quotient = 2x^2 − 4x − 5.

Steps (matching the three boxes):
1. First term: 2x^2 (since −8x^3 ÷ −4x = 2x^2)
2. Next term: −4x (since 16x^2 ÷ −4x = −4x)
3. Last term: −5 (since 20x ÷ −4x = −5)

Check: (−4x+5)(2x^2−4x−5) = −8x^3+26x^2−25, remainder 0.