which polynomial represents the algebra tile configuration shown?
a x^2 + 3x + 4
b x^2 + 3x − 4x
c −x^2 − 7
d −x^2 + 3x − 4

The correct answer is:   [D]:   "  − x²  +  3x  −  4  " .

Step-by-step explanation:

Start with the tile that has the largest exponent.

In this case, there is only one (1) tile with the exponent — " 2 " ;

 which is:   " − x² "  ;  

    →  and "2" is the "largest exponent" —  that corresponds to any variable among the titles given.

Then, look for the tiles with the "next largest exponent" (if any).

We find "x" ;  

 →   which has an "implied exponent" of " 1 " ;  since:  " x¹ = x " .

We see three (3) tiles — each with:  " + x "  values ;

so; we add them together since they are "like terms" with "positive signs" ;

      as follows:   + x + x + x  =  + 1x  +  1x  +  1x  =  " 3x "  .

{Note:  There is an "implied coefficient of " 1 " ;  for "x" values;  

              since:  "any value" ; multiplied by " 1 " ; results in that same values;

    so:  " x  =  x * 1  =  1 * x  =  1x  "  ;    ↔    " x = 1x " ;

The remaining four (4) tiles are simply "negative" unit values;

     with no "variables" ;  

    →  so;  We treat them as "-1 " values ;  

and "combine"  them ;

       →  and calculate ;  

→   since these values are "integers" ;  and as such; are "like terms" ;  

         →  as follows:

     − 1  −  1  −  1  − 1   =  

           (− 1  −  1)  −  1  − 1  =

                (−2 ) −  1  − 1  =

                    (−2 −  1 ) −  1  =

                       (−3) − 1  =   " − 4 " .

So, we combine all of our terms:

    →  to get:

        →       − x²  +  3x  −  4    ;

        →   which corresponds to:

        →  Answer choice:   [D]:   "  − x²  +  3x  −  4  " .

Hope this helps!

 Best wishes in your academic endeavors —

         and within the "" community!

the answer is in fact D

Step-by-step explanation: