Question

Could someone help me figure this out soon?

18y^2 +30y –92

i need to find the factored form.

Answer 1

\(\large \begin{align} \color{black}{
18y^2 +30y –92 \hspace{.33em}\\~\\
=2(9y^2 +15y –46) \hspace{.33em}\\~\\
=2\left(((3y)^2 2\cdot 3\cdot \dfrac{5}{2}y+\left(\dfrac{5}{2}\right)^2-\left(\dfrac{5}{2}\right)^2 –46\right) \hspace{.33em}\\~\\
=2\left(\left(3y+\dfrac{5}{2}\right)^2-\left(\dfrac{5}{2}\right)^2 –46\right) \hspace{.33em}\\~\\
=2\left(\left(3y+\dfrac{5}{2}\right)^2-\dfrac{209}{4}\right) \hspace{.33em}\\~\\
=2\left(\left(3y+\dfrac{5}{2}\right)^2-\left(\dfrac{\sqrt{209}}{2}\right)^2\right) \hspace{.33em}\\~\\
=2\left(\left(3y+\dfrac{5}{2}\right)-\left(\dfrac{\sqrt{209}}{2}\right)\right)\left(\left(3y+\dfrac{5}{2}\right)+\left(\dfrac{\sqrt{209}}{2}\right)\right) \hspace{.33em}\\~\\
}\end{align}\)