Question

Factorise:
$\frac{3}{2}{x}^2+16x+10$

Answer 1

$$\begin{gathered} \frac{3}{2}{x}^2+16x+10=\frac{3}{2}{x}^2+15x+x+10 \\ =3x\left(\frac{1}{2}x+5\right)+1\left(x+10\right) \\ =\frac{3}{2}x\left(x+10\right)+1\left(x+10\right) \\ =\left(x+10\right)\left(\frac{3}{2}x+1\right) \end{gathered}$$

Hence, factorisation of $\frac{3}{2}{x}^2+16x+10$ is $\left(x+10\right)\left(\frac{3}{2}x+1\right)$.