Problem 101 - Introductory Algebra for College Students

Question

What is factoring?

Step-by-Step Solution

Answer

Factoring is a mathematical process where a composite number, expression or polynomial is expressed as a product of simpler numbers, expressions or polynomials. For instance, 48 can be factored into \(2 \times 2 \times 2 \times 2 \times 3\). The polynomial \(x^2 + 5x + 6\) can be factored into \((x + 2) (x + 3)\).

Step 1: Explaining the Concept of Factoring

Factoring is essentially decomposing a number, expression or a polynomial into a product of other numbers, expressions or polynomials. In general, if 'b' and 'c' are two factors of 'a', it means \(a = b \times c\).

Step 2: Example of Factoring a Number

When we talk about factoring a number, we mean breaking it down into numbers that multiply together to give the original number. For example, the number 48 can be factored into \(2 \times 2 \times 2 \times 2 \times 3\). All these numbers multiplied together gives us the original number 48.

Step 3: Example of Factoring a Polynomial

In the context of polynomials, factoring means expressing a polynomial as the product of its factors. For example, the polynomial \(x^2 + 5x + 6\) can be factored into \((x + 2)(x + 3)\). These two polynomials multiplied together gives us the original polynomial \(x^2 + 5x + 6\).