Question

factor the given polynomial.

\\72y^4 + 64y^3 + 16y^2 = \\

Explanation:

Find the greatest common factor of the coefficients

Find the largest integer dividing \(72\), \(64\), and \(16\).

$$ \gcd(72, 64, 16) = 8 $$

Find the greatest common factor of the variable terms

Determine the lowest power of \(y\) present in all terms.

$$ \gcd(y^4, y^3, y^2) = y^2 $$

Combine to find the overall greatest common factor

Multiply the coefficient GCF and the variable GCF.

$$ \text{GCF} = 8y^2 $$

Divide each term by the greatest common factor

Divide each term of the polynomial by \(8y^2\).

$$
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$$

Write the completely factored polynomial

Express the polynomial as the product of the GCF and the remaining terms.

$$ 8y^2(9y^2 + 8y + 2) $$

Answer:

Factor the given polynomial.

\(72y^4 + 64y^3 + 16y^2 =\) <blank>\(8y^2(9y^2 + 8y + 2)\)</blank>