Question

introduction homework (standard 0)
score: 6/28 answered: 6/25
question 7
factor the polynomial below by factoring out the gcf:
$4x^5y^5 + 2x^4y^6 + 2x^3y^4$
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Explanation:

Step1: Find GCF of coefficients

The coefficients are 4, 2, 2. The GCF of 4, 2, 2 is 2.

Step2: Find GCF of \(x\)-terms

For \(x^5\), \(x^4\), \(x^3\), the GCF is \(x^3\) (since the lowest power of \(x\) is 3).

Step3: Find GCF of \(y\)-terms

For \(y^5\), \(y^6\), \(y^4\), the GCF is \(y^4\) (since the lowest power of \(y\) is 4).

Step4: Factor out GCF

The GCF is \(2x^3y^4\). Now divide each term by \(2x^3y^4\):

• \(\frac{4x^5y^5}{2x^3y^4}=2x^2y\)
• \(\frac{2x^4y^6}{2x^3y^4}=xy^2\)
• \(\frac{2x^3y^4}{2x^3y^4}=1\)

So the factored form is \(2x^3y^4(2x^2y + xy^2 + 1)\).

Answer:

\(2x^3y^4(2x^2y + xy^2 + 1)\)