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Chapter 0: Problem 129

What does it mean to factor completely?

Short Answer

Expert verified
To factor completely means to express a number or expression as a product of prime numbers (for numbers) or irreducible polynomials (for expressions). For instance, the number 12 can be factored completely into 2x2x3.

Step by step solution

01

Define Factoring

Factoring in mathematics means expressing a given number or expression as a product of two or more other numbers or expressions. These numbers or expressions are called the 'factors' of the original number or expression.
02

Understand the Concept of Prime Numbers

Prime numbers are those numbers that have only two factors: 1 and the number itself. They cannot be expressed as the product of other numbers. Examples of prime numbers include 2, 3, 5, 7, 11, and so on.
03

Define 'Factoring Completely'

When a number or expression is expressed as the product of prime numbers (for numbers) or irreducible polynomials (for expressions), it is said to be 'factored completely'.
04

Apply the Concept Through Examples

For instance, if asked to factor the number 12 completely, the process would be: 12 can be factored into 3x4, but it's not factored completely because 4 isn't a prime number. Factoring 4 further gives 2x2. So, the completely factored form of 12 is 2x2x3, which are all prime numbers.

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Most popular questions from this chapter

What is an algebraic expression? Give an example with your explanation.

Simplify by reducing the index of the radical. $$ \sqrt[12]{x^{4} y^{8}} $$

Factor Completely. $$(x+y)^{4}-100(x+y)^{2}$$

Will help you prepare for the material covered in the next section. A. Use a calculator to approximate \(\sqrt{300}\) to two decimal places. B. Use a calculator to approximate \(10 \sqrt{3}\) to two decimal places. C. Based on your answers to parts (a) and (b), what can you conclude?

Factor Completely. $$12 x^{2}(x-1)-4 x(x-1)-5(x-1)$$
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