ElectricPavlov

The factored form would be  (x-1)(x+1)      ....if you do the multiplication , you will get  x^2 + (0)x -1  or just x^2 -1 

distance / rate = time 

d/40 = d/55 + 25/60    <=====  Given ... solve for 'd' 

3/440 d = 25/60 

d = 61  1/9 miles 

  The set of points 5 units away from 2,7  is a circle :

(x-2)^2 + (y-7)^2 = 5^2  

The line might intersect at ONE point (tangent) or TWO Points .

   Plug in the value of the line into the circle equation 

      ( x-2)^2 + ( 5x-28 -7)^2 = 5^2 

Expand 

          x^2 - 4x + 4  + 25x^2 -350x  + 1225  = 25 

 Solve for 'x'

            26x^2 - 354 x + 1204 = 0    Use quadratic formula to find x = 7 and  6.61538   ( two points) ....use these values ofr 'x' in the line equation to find the corresponding ' y ' coordinates  = 7 and  5.07692

See attached image:

I will assume you meant THIS: 

 (x^3 + x^2 + x + 1)(x^4 + 3x^3 + 8x^2 + 7x + 1)

When you multiply the two polynomials you will get these parts :

x^2 * 1     +     x * 7x     +     1 * 8x^2       =     16 x^2 

So the coefficient will be ' 16 ' 

The 'x' coefficient  willl come from  the multiplication of the two polynomial factors :   (1 * 8x)  + (7 * x ) = 15x 

so the coefficient of 'x' will be  '15' 

x + y = 2      then ( x + y)^2 = 4                       and  (x+y)^3 = 8 

                              x^2 + y^2 + 2xy = 4 

(x+y)^3 =8   =  x^3 + y^3 + 3xy^2 + 3x^2y = x^3 + y^3  + 3xy ( x + y)      sub in for x+ y    and   x^3 + y^3 

               8 =  5 + 6 xy 

               3 = 6 xy 

                1/2 = xy                 Now sub in to the red equation 

            x^2 + y^2  + 2 ( 1/2) = 4 

                   x^2 + y^2 = 3 

One base is 12  and the other is  (16+12) = 28 

median = (12+28) / 2 = 20 units 

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