Question

# Create your own trinomial and find the factors.

Factors and multiples
Create your own trinomial and find the factors.

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 $$\displaystyle{x}={\frac{{-{3}}}{{{2}}}}$$