Find length if the width is x+5 cm and height is x-3 cm

Question

The volume of a box is 4x² +13x²-50x-75 cubic centimeters. Find the length if the width is x+5 centimeters and the height is x-3 centimeters.

length =

width =

thank you to anyone who can help!

Answer 1

To find the length, you have to divide the volume by each dimension. You can do this by long division or synthetic division. I will use synthetic division. For the zero, we use the first factor, x=-5 (You could start with the other one, it doesn't matter to order)

-5 | 4 13 -50 -75

-20 35 75

4 -7 -15 0

The remainder is 0, which is what we would hope for! Now take this result and divide by the other zero. x=3

3 | 4 -7 -15

12 15

4 5 0

Another zero remainder which is good news. The solution is 4x+5