Problem 123 Using an example, explain how to... [FREE SOLUTION]

91影视

Precalculus Essentials

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

5 Edition

Chapter 0: Problem 123

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

Short Answer

Expert verified

The factored form of the polynomial $4x^3 + 8x^2$ after factoring out the greatest common factor is $4x^2(x+2)$.

Step by step solution

Identify the Polynomial and its Coefficients

Let's factor out the greatest common factor from the polynomial $4x^3 + 8x^2$. Here, the two coefficients are 4 and 8.

Find the Greatest Common Factor

The next step is to determine the Greatest Common Factor (GCF) of the coefficients. The GCF of 4 and 8 is 4. In terms of powers of $x$, $x^3$ and $x^2$ are the terms involved in the polynomial. The GCF is the lower power i.e. $x^2$. Hence, the GCF of the polynomial $4x^3 + 8x^2$ is $4x^2$.

Divide the polynomial by the GCF

Divide each term of the polynomial by the greatest common factor. Thus, divide $4x^3$ by $4x^2$ to give $x$, and divide $8x^2$ by $4x^2$ to give 2.

Write the factored form

Finally the polynomial $4x^3 + 8x^2$ factored out by its greatest common factor is written as GCF times the resulting polynomial. This means $4x^3 + 8x^2 = 4x^2(x+2)$ is the factored form.

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91影视

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

Short Answer

Step by step solution

Identify the Polynomial and its Coefficients

Find the Greatest Common Factor

Divide the polynomial by the GCF

Write the factored form

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