I just can't answer this can someone help?

[wattlemelon]

I've been trying to answer 1 - 3 but i can only answer 4. Any help would be appreciated thank you.

 

[Dr.Peterson]

View attachment 24430
I've been trying to answer 1 - 3 but i can only answer 4. Any help would be appreciated thank you.

Please show us what is going wrong when you try #1. At least show the result of the first synthetic division; ideally I'd want to see your work in case you are just making some silly error in the process.

The more you show, the more effective help we can give:

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[Steven G]

When you multiply the 3 dimensions you get 2x^3 + 15x^2 + 22x-15.

So (2x-1)(x+3)(unknown) = 2x^3 + 15x^2 + 22x-15
(2x^2 - 5x - 3)(unknown) = 2x^3 + 15x^2 + 22x-15
(2x^2 - 5x - 3) is a 2nd degree polynomial and 2x^3 + 15x^2 + 22x-15 is a 3rd degree polynomial.

It really needs to be clear that the unknown must be a 1st degree polynomial which is in the form ax+b
What do you multiply 2x^2 by to get 2x^3? What do you multiply -3 by to get -15? These two answers will give you the unknown.
Of course I found the missing factor without using synthetic division.

 

[kunal_kumar16]

View attachment 24430
I've been trying to answer 1 - 3 but i can only answer 4. Any help would be appreciated thank you.

I think the real roots are... x>=1.
And the third dimension is... x+5.

 

[Dr.Peterson]

I think the real roots are... x>=1.
And the third dimension is... x+5.

No, there are three real roots, only one of which is positive; and x+5 is not a "dimension", though it is part of the answer.

We're still waiting for the OP, @wattlemelon, to show what they know about synthetic division (or to follow Jomo's alternative approach).