The fence around a quadrilateral-shaped pasture is 3a^2+15a+9 long. three sides of the fence have the following lengths: 5a, 10a-2, a^2-7. what is the length of the fourth side of the fence?

The unknown side is 2a^2+18

Step-by-step explanation:

Perimeter is adding all the sides

We have 4 sides so we add all 4 sides.  We will call the 4th side x.  The perimeter is 3a^2+15a+9.  The 3  known sides are 5a, 10a-2, a^2-7.

5a+10a-2 + a^2-7 + x = 3a^2 +15a+9

Combine like terms

15a-9 + a^2 + x = 3a^2 +15a+9

Subtract 15a from each side

15a-15a-9 + a^2 + x = 3a^2 +15a-15a+9

-9+ a^2 + x = 3a^2 +9

Add 9 to each side

-9+9+ a^2 + x = 3a^2 +9+9

a^2 +x = 3a^2 +18

Subtract a^2 from each side

a^2  -a^2+x = 3a^2-a^2 +18

x = 2a^2 +18

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0