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Polynomial

Practice  6-1 Polynomial Functions

Find a cubic model for each function. Then use your model to estimate the
value of y when  x = 7.

Write each polynomial in standard form. Then classify it by degree and by
number of terms .

24. The lengths of the sides of a triangle are x + 4 units, x units, and
x + 1 units. Express the perimeter of the triangle as a polynomial in
standard form.

25. Find a cubic function to model the data below (Hint: Use the number
of years past 1940 for x) Then use the function to estimate the average
monthly Social Security Benefit for a retired worker in 2005.

Average Monthly Social Security Benefits, I940-1999

Year
Amount
(in dollars

25, Find a cubic function to model the data below. (Hint: Use x to represent
the gestation period.) Then use the function to estimate the longevity of
an animal with a gestation period of 151 days.

Gestation and Longevity of Certain Animals

Animal Rat Squirrel Pig Cow Elephant
Gestation
(in days)
 
Longevity
{in years

Practice 6 -2 Polynomials and Linear Factors

For each function, determine the zeros, State the multiplicity of any
multiple zeros.

Write each function in standard form.

9. A rectangular box is 24 in. long,12 in. wide, and 18 in. high. If each
dimension is increased by x in., write a polynomial function in standard
form modeling the volume V of the box,

Write a polynomial function in standard form  with the given zeros

13. -2 multiplicity 3

Write each expression as a polynomial in standard form

Write each function in factored form . Check by multiplication.

Find the zeros of each function. Then graph the function .

Find the relative maximum, relative minimum, and zeros of each function.

Write each polynomial in factored form. Check by multiplication.

28. A rectangular box has a square base . The combined length of a side of
the square base, and the height is 20 in. Let x be the length of a side of
the base of the box.

a. Write a polynomial function in factored form modeling the volume
V of the box.

b, What is the maximum possible volume of the box?

Practice 6-3 Dividing Polynomials  

Determine whether each binomial is a factor of .

Divide using synthetic division .

Use synthetic division and the Remainder Theorem to find P(a).

Divide using long division. Check your answers

Use synthetic division and the given factor to completely factor each
polynomial function.

Divide.

31. A box is to be mailed. The volume in cubic inches of the box
can be expressed as the product of its three dimensions:
. The length is x - 8. Find linear
expressions for the other dimensions Assume that the width is
greater than the height.

Reteaching 6 - 4 Solving Polynomial Equations

OBJECTIVE: Solving polynomial equation by  MATERIALS: None
factoring

Example

Solve by factoring. Find all complex roots .

   
     
Since 2 is a common factor to each
term, factor out 2.
     
Factor the remaining cubic expression.
     
Use the Zero- Product Property .
     
Solve each equation for x. Use the
Quadratic
Formula when necessary
     
   
     
Simplify .
     
The solutions are -2 and .    

Exercises

Solve each equation by factoring. Find all complex roots.

Practice 6 -4 Solving Polynomial Equations

Factor the expression on the left side of each equation. Then solve
the equation.

17. Over 3 yr, Lucia saved$ 550,$ 600,and $650 from baby-sitting jobs. The
polynomial represents her savings, with interest,
after 3 yr. The annual interest rate equals x -1. Find the interest
needed so that she will have $2000 after 3 yr.

Solve each equation by graphing. Where necessary, round to the
nearest hundredth.

24, The product of three consecutive integers n - 1,n,and n +1 is -336.
Write and solve an equation to find the numbers.

Factor each expression

Solve each equation.

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