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
t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?
