Write an equation of a line that is parallel to y = 5. Write an equation of a line that is perpendicular to y = 5. What do you notice about the equation of the
perpendicular line?

The perpendicular line intersects with the parallel line.

Perpendicular lines have negative reciprocal slopes to parallel lines, so it intersects with the parallel line.

Parallel line: y = 5x + 3

Perpendicular line: y = -1/5x - 4

(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