Question

# Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor is necessary: 21m^{2}+13mn+2n^{2}

Applications of integrals
Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor is necessary:
$$\displaystyle{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}$$

2021-04-01
Step 1
To factorise: $$\displaystyle{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}$$
Solution:
$$\displaystyle{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}$$
On simplifying further, we get:
$$\displaystyle{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}={21}{m}^{{{2}}}+{\left({7}{m}{n}+{6}{m}{n}\right)}+{2}{n}^{{{2}}}$$
$$\displaystyle={\left({21}{m}^{{{2}}}+{7}{m}{n}\right)}+{\left({6}{m}{n}+{2}{n}^{{{2}}}\right)}$$
=7m(3m+n)+2n(3m+n)
=(3m+n)(7m+2n)
$$\displaystyle\Rightarrow{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}={\left({3}{m}+{n}\right)}{\left({7}{m}+{2}{n}\right)}$$
Step 2
Result:
$$\displaystyle{21}{m}^{{{2}}}+{13}{m}{n}+{2}{n}^{{{2}}}={\left({3}{m}+{n}\right)}{\left({7}{m}+{2}{n}\right)}$$