Question

Create your own trinomial and find the factors.

Factors and multiples
ANSWERED
asked 2021-08-02
Create your own trinomial and find the factors.

Answers (1)

2021-08-03
Step 1
a) \(\displaystyle{6}{x}^{{{2}}}+{x}-{12}\)
Factorization:
\(\displaystyle{6}{x}{12}={72}\)
\(\displaystyle{72}={9}{x}{8}\)
\(\displaystyle{6}{x}^{{{2}}}+{9}{x}-{8}{x}-{12}={0}\)
\(\displaystyle{3}{x}{\left({2}{x}+{3}\right)}-{4}{\left({2}{x}+{3}\right)}={0}\)
\(\displaystyle{\left({2}{x}+{3}\right)}{\left({3}{x}-{4}\right)}={0}\)
\(\displaystyle{2}{x}+{3}={0}\) or \(\displaystyle{3}{x}-{4}={0}\)
\(\displaystyle{x}={\frac{{-{3}}}{{{2}}}}{x}={\frac{{{4}}}{{{3}}}}\)
Step 2
Method:
\(\displaystyle{x}={\frac{{-{b}\pm\sqrt{{{b}^{{{2}}}-{4}{a}{c}}}}}{{{2}{a}}}}\)
\(\displaystyle{x}={\frac{{-{1}\pm\sqrt{{{1}+{4}{x}{6}{x}{12}}}}}{{{2}{x}{6}}}}\)
\(\displaystyle{x}={x}={\frac{{-{1}\pm{17}}}{{{12}}}}\)
\(\displaystyle{x}={\frac{{{16}}}{{{12}}}}\) or \(\displaystyle{x}={\frac{{-{18}}}{{{12}}}}\)
\(\displaystyle{x}={\frac{{{4}}}{{{3}}}}\) or \(\displaystyle{x}={\frac{{-{3}}}{{{2}}}}\)
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