# Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary. 3y^3+24y^2+9y

Question
Polynomial factorization
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.
$$\displaystyle{3}{y}^{{3}}+{24}{y}^{{2}}+{9}{y}$$

2021-01-17
Step 1
Given: The polynomial $$\displaystyle{3}{y}^{{3}}+{24}{y}^{{2}}+{9}{y}$$
To determine: The factorization of the polynomial.
Step 2
Explanation:
Factorizing the polynomial,
$$\displaystyle{3}{y}^{{3}}+{24}{y}^{{2}}+{9}{y}$$
$$\displaystyle={3}{\left({y}^{{3}}+{8}{y}^{{2}}+{3}{y}\right)}{\left[{t}{a}{k}\in{g}{3}{a}{s}{c}{o}{m}{m}{o}{n}\right]}$$
$$\displaystyle={3}{y}{\left({y}^{{2}}+{8}{y}+{3}\right)}{\left[{t}{a}{k}\in{g}{y}{a}{s}{c}{o}{m}{m}{o}{n}\right]}$$
Result: $$\displaystyle{3}{y}^{{3}}+{24}{y}^{{2}}+{9}{y}={3}{y}{\left({y}^{{2}}+{8}{y}+{3}\right)}$$.

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