( 2x^4+2x^3+x^2-x-1 ) \ ( x^2-x-1 )

Step-by-step explanation:

We want perform the following polynomial division.

We carry out the polynomial division in the attachment to obtain:

See attachment;

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

what level of math? also i don't need to be paid if i can you.