Using synthetic division, what is the width of the rectangle? Brainliest!! 5 stars, thanks.

Hi there!

**Work pictured below**

Since x + 3 is one of the factors, set it equal to zero to find the root:

x + 3 = 0

x = -3

Use -3 in the synthetic division process to solve for the width.

Use the coefficients of 5x³ + 19x² + 6x - 18 to do synthetic division:

5, 19, 6, -18

To do synthetic division, arrange the numbers in the polynomial as shown with the root outside of the diagram.

1. Bring down the first number

2. Multiply by the root and add that number to the next number. Bring the sum down to the bottom.

3. Repeat until finished with all numbers. If a number is a perfect root, it will have a remainder of 0 at the last number.

In this instance, doing so produced the numbers 5, 4 and -6. There was also no remainder as the last number produced 0. Therefore, the width of the rectangle is:

5x² + 4x - 6 **First term is always one degree LESS than you started with**

5x^2 + 4x - 6

Step-by-step explanation:

(5x^3 + 19x^2 + 6x - 18)/(x + 3)

-3  |   5   19   6   -18

            -15  -12  18

         5   4   -6     0

(5x^3 + 19x^2 + 6x - 18)/(x + 3) = 5x^2 + 4x - 6

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