Question

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.

Answer 1

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!