The volume of the rectangular prism below is 30x3 + 35x2 + 10x factor to find the possible expressions for length,width and height of the prism.

30x³ + 35x² + 10x factorised is 5x(2x + 1)(3x +2). To find this, you first want to take out a common factor to be left with a quadratic equation. In this case, we can factor out 5x to be left with 6x² + 7x + 2.

Now we can factorise 6x² + 7x + 2 by finding factors of 6 that add together to make 7 when one of them is multiplied by 2. These are 3 and 2, which is how we end up with (2x + 1) and (3x + 2). Let me know if you would like me to go more indepth about how I found this.

Then you just put these with the 5x and you get 5x(2x + 1)(3x + 2), which are possible expressions for the length, width, and height.
I hope this helps!

Equivalent equations have the same solution. You can create equivalent equations by performing the same operations on each side of the equation. You can check for equivalence by finding the solution for each equation.

hope this helps