Question

Choose from the column on the right the item that corresponds to the type of polynomial. Choices may be used more than once. a) Polynomial with a common factor b) Difference of two squares c) Sum of two cubes d) Difference of two cubes e) Perfect-square trinomial I) None of these $$\text{_____}c^{12}+1$$

Name: Problem 5, Chapter 5: Intermediate Algebra : Concepts and Applications
Uploaded: 2020-07-18T12:01:53-08:00
Duration: 42 s
Channel: Ankit Gupta
Description: Choose from the column on the right the item that corresponds to the type of polynomial. Choices may be used more than once. a) Polynomial with a common factor b) Difference of two squares c) Sum of two cubes d) Difference of two cubes e) Perfect-square trinomial I) None of these c^12+1

   Choose from the column on the right the item that corresponds to the type of polynomial. Choices may be used more than once.
a) Polynomial with a common factor
b) Difference of two squares
c) Sum of two cubes
d) Difference of two cubes
e) Perfect-square trinomial
I) None of these

$$\text{_____}c^{12}+1$$

Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger,… 10th Edition

Chapter 5, Problem 5

Instant Answer

Solved by Expert Ankit Gupta

07/18/2020

Step 1

The given polynomial is $c^{12}+1$. Show more…

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Choose from the column on the right the item that corresponds to the type of polynomial. Choices may be used more than once. a) Polynomial with a common factor b) Difference of two squares c) Sum of two cubes d) Difference of two cubes e) Perfect-square trinomial I) None of these $$\text{_____}c^{12}+1$$

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Key Concepts

Sum of Two Cubes Identity

The sum of two cubes identity is a specific factorization formula used when a polynomial can be written as a^3 + b^3. The formula a^3 + b^3 = (a + b)(a^2 - ab + b^2) allows for the polynomial to be factored into a linear factor and a quadratic factor. This technique is particularly useful when an expression can be rewritten to match the sum of two cubes form, as in rewriting c^12 + 1 as (c^4)^3 + 1^3.

Polynomial Factorization

Polynomial factorization involves rewriting a polynomial as a product of two or more simpler polynomials. This process is fundamental in algebra as it can simplify expressions, solve polynomial equations, and reveal properties of the polynomial, such as its roots. Recognizing different types of polynomials, such as those that can be factored by common methods, is a central skill in this area.

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