Find the remainder when 2x3-3x2+ 4x +1 is divided by (x -1/2)

The first step is wrong and he must , instead of using the additive invserse property, start with the commutative property to show -8.3 - 4.4 + 9.2 + 3.7, and continue with the associate property to show (-8.3 - 4.4) + (9.2 + 3.7).

Explanation:

Start by rearranging the table for better understanding of each step.

Step   Work                              Reasoning

   0    −8.3 + 9.2 − 4.4 + 3.7     Original problem

   1     −8.3 + 9.2 + 4.4 + 3.7      Additive inverse

   2    −8.3 + 4.4 + 9.2 + 3.7      Commutative property

   3     −8.3 + (4.4 + 9.2 + 3.7)   Associative property

   4     −8.3 + 17.3                      Simplify

   5       9                                   Simplify

In the first step, it was used the addtive inverse property and the number -4.4 was changed to 4.4. This is a mistake because that changes the value of the expression. Any step that you use to solve the expression must not change its value but just lead step-by-step to the final value of the whole expression.

The additive inverse property is used in equations in order to isolate a variable by adding the additive inverse of a number to both sides of the equation. This is based in the addtiion or subtraction property of the equality which state that you can add or subtract the same number to both sides of the equation without modifiying the value.

Then, the feedback to Allen may that that the first step is wrong, and he must , instead, start with the commutative property, then associate the two negative numbers, -8.3 and -4.4. With that the correct steps are:

Step   Work                                Reasoning

   0    −8.3 + 9.2 − 4.4 + 3.7        Original problem

    1    −8.3 - 4.4 + 9.2 + 3.7        Commutative property

    2   (−8.3 - 4.4) + (9.2 + 3.7)    Associative property

   3     − 12.7 + 12.9                     Simplify

   4       0.2                                 Simplify

The final value is 0.2.