Answers

1. The width of the rectangle using synthetic division is; 5x² + 4x – 6.

   What is the width of the rectangle whose area is 5x³+19x²+6x-18?

   From the task content; the width of the rectangle whose area and length are as given can be evaluated as follows;

   Area = Length × width

   Hence, width = Area/length.

   Thus, given an area of (5x³ + 19x² + 6x – 18) and a length of (x + 3), to find the width, we have

   width = (5x³ + 19x² + 6x – 18) / (x + 3)

   Through the coefficients of the polynomial, we can apply synthetic division to find the quotient as shown below.

   5  19  6  -18 | -3

     -15 -12  18

   _____________

   5   4   -6  0

   Thus, the given values below the line are the coefficients of the width. So, we have the rectangle’s width as (5x² + 4x – 6) units.

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   The complete question is –

   The area of a rectangle is 5×3+19×2+6x-18 with length x + 3. Using synthetic division, what is the width of the rectangle?

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