Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x 5 - 8x 3 + 24x 2 + 12x + 40) (x + 4)

Answer 1

We can divide the polynomial (x⁵ - 8x³ + 24x² + 12x + 40) by (x + 4) using synthetic division.

What is synthetic division?

In the case of dividing by a linear factor, the synthetic division is a shorthand, or quicker, a technique of polynomial division.

We have a polynomial:

(x⁵ - 8x³ + 24x² + 12x + 40)

Which need to divide by  (x + 4)

= (x⁵ - 8x³ + 24x² + 12x + 40) ÷ (x + 4)

$\rm \mathrm{Coefficients\:of\:the\:numerator\:polynom}$

$\rm 1\:\:-8\:\:24\:\:12\:\:40$

$\rm \begin{matrix}\texttt{\:\:-4 | \:\:\:1\:\:\:0\:\:-8\:\:24\:\:12\:\:40}\\ \texttt{\:\:\:\:\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}$

            1

$\rm \begin{matrix}\texttt{\:\:-4 | \:\:\:1\:\:\:0\:\:-8\:\:24\:\:12\:\:40}\\ \texttt{\:\:\:\:\underline{\:\:\:\:\:\:-4\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}\\ \texttt{\:\:\:\:\:\:\:\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}$

Similarly,

$\rm \begin{matrix}\texttt{\:\:-4 | \:\:\:1\:\:\:0\:\:-8\:\:24\:\:12\:\:40}\\ \texttt{\:\:\:\:\underline{\:\:\:\:\:\:-4\:\:16\:-32\:\:32-176}}\\ \texttt{\:\:\:\:\:\:\:\:1\:\:-4\:\:\:8\:\:-8\:\:44-136}\end{matrix}$

The remainder is -136

The answer will be:

$\rm x^4-4x^3+8x^2-8x+44-\dfrac{136}{x+4}$

Thus, we can divide the polynomial (x⁵ - 8x³ + 24x² + 12x + 40) by (x + 4) using synthetic division.

Learn more about the synthetic division here:

brainly.com/question/11850611

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