What is the quotient

 -2, 5

Step-by-step explanation:

                                      3x²  -  2x  + 5  

x² + 3x + 1 ) 3x⁴ + 7x ³ + 2x² + 13x + 5

                - (3x⁴ + 9x³ + 3x²)    ↓     ↓

                           -2x³  -  x²  + 13x    ↓

                        - (-2x³ - 6x²  -  2x)   ↓

                                     5x²  + 15x + 5

                                   - (5x² + 15x + 5)

                                                         0

step-by-step explanation:

circumference divided by 3.141592654 then timesthe radius twice

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4