Explain how you could determine the dimensions of the cut square if the desired volume was 3600 cubic inches

Writing in Math Use the information on page 369 to explain how solving a polynomialequation can help you find dimensions. Explain how you could determine the dimensions of thecut square if the desired volume was 3600 cubic inches. Explain why there can be more thanone square that can be cut to produce the same volume. 6-6
Solving Polynomial Equations
Main Ideas
Factor polynomials.
• Solve polynomial
equations by
factoring
32 – 2x
GET READY for the Lesson
The Taylor Manufacturing Company
50 – 2x
makes
open metal boxes of various sizes.
Each sheet of metal is 50 inches long and
32 inches wide. To make a box, a square is
cut from each corner
The volume of the box depends on the
side length of the cut squares. It is given by V(x) = 4×3 -164.×2 +
1600x. You can solve a polynomial equation to find the dimensions of
the square to cut for a box with specific volume.
New Vocabulary
quadratic form
Factor Polynomials Whole numbers are factored using prime numbers.
For example, 100 = 2.2.5.5. Many polynomials can also be factored.
Their factors, however, are other polynomials. Polynomials that cannot
be factored are called prime. One method for finding the dimensions of
the square to cut to make a box involves factoring the polynomial that
represents the volume.
The table below summarizes the most common factoring techniques
used with polynomials. Some of these techniques were introduced in
Lesson 5-3. The others will be presented in this lesson.
CONCEPT SUMMARY
Number of Terms Factoring Technique
any number Greatest Common Factor (GCF)
two
Difference of Two Squares
Sum of Two Cubes
Difference of Two Cubes
three Perfect Square Trinomials
General Trinomials
Grouping
Factoring Techniques
General Case
a>b2+ 2a2b – 40b2ab(a2b + 20 – 46)
02- 62 = (a + b)(a – b)
a3 + b3 = (a + b)(a2 – ab + b2)
a3-b3 = (a – b)(a2 + ab + b2)
q2 + 2ab + b2 = (a + b)2
02 – 2ab + b2 = (a – b)2
acx2 + (ad + bc)X + bd = (ax + b)(a + d)
ax + bx + ay + by = x(a + b) + y(a + b)
= (a + b)(x + 1)
four or more
Whenever you factor a polynomial, always look for a common factor
first. Then determine whether the resulting polynomial factor can be