Two adjacent sides of a parallelogram have length of 5 cm and 11 cm. Each of the two diagonals divide the parallelogram into two congruent triangles. If the lengths of the diagonals are the smallest and the greatest possible prime values (as sides of the triangles), then what is the sum of the lengths of the diagonals ?

20 cm

Step-by-step explanation:

Since the diagonals have to be prime numbers, and they have to be able to be sides of a triangle, the formula would be 6<x<16. The prime numbers in this group are 7, 11, and 13. Since 7 is the smallest prime number in this group and 13 is the largest, 7+13=20.

(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