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
Polynomial long division can be used to divide a polynomial by any polynomial with equal or lower degree. See
[link] and
[link].
The Division Algorithm tells us that a polynomial dividend can be written as the product of the divisor and the quotient added to the remainder.
Synthetic division is a shortcut that can be used to divide a polynomial by a binomial in the form
See
[link],[link], and
[link].
Polynomial division can be used to solve application problems, including area and volume. See
[link].
Questions & Answers
if three forces F1.f2 .f3 act at a point on a Cartesian plane in the daigram .....so if the question says write down the x and y components ..... I really don't understand
a fixed gas of a mass is held at standard pressure temperature of 15 degrees Celsius .Calculate the temperature of the gas in Celsius if the pressure is changed to 2×10 to the power 4