The greatest integer function or floor function : r → z is defined as follows: for every real number c er, is the greatest integer which is less or equal to r. using the floor function and the basic arithmetic operations, find an explicit formula for the quotient and remainder of two integers. prove your result.

Demonstrate the proof of your new polynomial identity through an algebraic proof and a numerical proof in an engaging way! make it so the whole world wants to purchase your polynomial identity and can't imagine living without it! you must: label and display your new polynomial identity prove that it is true through an algebraic proof, identifying each step demonstrate that your polynomial identity works on numerical relationships create your own using the columns below. see what happens when different binomials or trinomials are combined. square one factor from column a and add it to one factor from column b to develop your own identity. column a column b (x − y) (x2 + 2xy + y2) (x + y) (x2 − 2xy + y2) (y + x) (ax + b) (y − x) (cy + d)

Find the slope of the line passing through a pair of points

Luke started a weight-loss program. the first week, he lost x pounds. the second week, he lost pounds less than times the pounds he lost the first week. the third week, he lost 1 pound more than of the pounds he lost the first week. liam started a weight-loss program when luke did. the first week, he lost 1 pound less than times the pounds luke lost the first week. the second week, he lost 4 pounds less than times the pounds luke lost the first week. the third week, he lost pound more than times the pounds luke lost the first week.