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: \(\displaystyle{3}{y}^{{3}}+{24}{y}^{{2}}+{9}{y}={3}{y}{\left({y}^{{2}}+{8}{y}+{3}\right)}\).

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: \(\displaystyle{3}{y}^{{3}}+{24}{y}^{{2}}+{9}{y}={3}{y}{\left({y}^{{2}}+{8}{y}+{3}\right)}\).