Questions: Factor out the greatest common factor. 17 q^4 + 34 q^2 =

Factor out the greatest common factor. 17 q^4 + 34 q^2 =
Transcript text: Factor out the greatest common factor. \[ 17 q^{4}+34 q^{2}= \]
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Solution

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Solution Steps

To factor out the greatest common factor (GCF) from the given polynomial, we first identify the GCF of the coefficients and the variables. The GCF of 17 and 34 is 17, and the lowest power of \( q \) in the terms is \( q^2 \). Therefore, the GCF is \( 17q^2 \). We then divide each term by \( 17q^2 \) and factor it out.

Step 1: Identify the Greatest Common Factor (GCF)

To factor out the greatest common factor (GCF) from the polynomial \( 17q^4 + 34q^2 \), we first identify the GCF of the coefficients and the variables. The GCF of 17 and 34 is 17, and the lowest power of \( q \) in the terms is \( q^2 \). Therefore, the GCF is \( 17q^2 \).

Step 2: Factor Out the GCF

Next, we divide each term by \( 17q^2 \) and factor it out: \[ 17q^4 + 34q^2 = 17q^2(q^2 + 2) \]

Final Answer

\[ \boxed{17q^2(q^2 + 2)} \]

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