(2x3 - 5x2 + 3x + 7) /(x - 2)

2x^2 - x + 1 + 9/(x - 2)

Step-by-step explanation:

Long division:

x - 2 )2x^3 - 5x^2 + 3x + 7 (2x^2 - x  + 1 <Quotient.

        2x^3 - 4x^2

                  -x^2 + 3x

                  -x^2 + 2x

                               x + 7

                                x - 2

                                    9  <Remainder.

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.