Using synthetic division to divide a second-degree polynomial
Use synthetic division to divide
by
Begin by setting up the synthetic division. Write
and the coefficients.
Bring down the lead coefficient. Multiply the lead coefficient by
Continue by adding the numbers in the second column. Multiply the resulting number by
Write the result in the next column. Then add the numbers in the third column.
The result is
The remainder is 0. So
is a factor of the original polynomial.
Using polynomial division to solve application problems
Polynomial division can be used to solve a variety of application problems involving expressions for area and volume. We looked at an application at the beginning of this section. Now we will solve that problem in the following example.
Using polynomial division in an application problem
The volume of a rectangular solid is given by the polynomial
The length of the solid is given by
and the width is given by
Find the height of the solid.
There are a few ways to approach this problem. We need to divide the expression for the volume of the solid by the expressions for the length and width. Let us create a sketch as in
[link] .
We can now write an equation by substituting the known values into the formula for the volume of a rectangular solid.
To solve for
first divide both sides by
Now solve for
using synthetic division.
The quotient is
and the remainder is 0. The height of the solid is
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
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how does the stomach protect itself from the damaging effects of HCl
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature