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Chapter 0: Problem 101

Using an example, explain how to factor out the greatest common factor of a polynomial.

Short Answer

Expert verified
The polynomial \(4x^3 + 8x^2\) factors to \(4x^2(x + 2)\) using the GCF of \(4x^2\).

Step by step solution

01

Identifying the Polynomial and its Terms

Let's take the polynomial \(4x^3 + 8x^2\). This polynomial has two terms - \(4x^3\) and \(8x^2\). Each term is a product of a numerical coefficient and a power of \(x\).
02

Finding the Greatest Common Factor

The next step is to identify the greatest common factor (GCF) of the terms of the polynomial. In this case, the GCF is \(4x^2\), which is the highest factor that is common to both terms.
03

Factoring Out the GCF

Next, each term of the polynomial is divided by the GCF, resulting in a factored polynomial. Thus, \(4x^3\) divided by \(4x^2\) gives \(x\), and \(8x^2\) divided by \(4x^2\) gives \(2\). The fully factored polynomial is therefore \(4x^2(x + 2)\).

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