Questions: Factor out the GCF from the polynomial. 6y^7 + 2y^3

Factor out the GCF from the polynomial. 6y^7 + 2y^3
Transcript text: Factor out the GCF from the polynomial. \[ 6 y^{7}+2 y^{3} \]
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Solution

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Solution Steps

Step 1: Identify the Greatest Common Factor (GCF)

To factor the polynomial \(6y^7 + 2y^3\), we first identify the greatest common factor (GCF) of the coefficients and the variable terms. The coefficients are 6 and 2, and the GCF of these numbers is 2. The variable terms are \(y^7\) and \(y^3\), and the GCF of these terms is \(y^3\).

Step 2: Factor Out the GCF

We factor out the GCF, \(2y^3\), from each term in the polynomial:

\[ 6y^7 + 2y^3 = 2y^3 \cdot \left(\frac{6y^7}{2y^3} + \frac{2y^3}{2y^3}\right) \]

Simplifying inside the parentheses:

\[ = 2y^3 \cdot (3y^4 + 1) \]

Final Answer

The factored form of the polynomial is:

\[ \boxed{2y^3(3y^4 + 1)} \]

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