Question

factorise the following(middle term splitting)
i)6x^2+7x-3
ii)84-2r-2r^2

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right).6{\mathrm{x}}^2+7\mathrm{x}-3 \\ =6{\mathrm{x}}^2+9\mathrm{x}-2\mathrm{x}-3 \\ =3\mathrm{x}\left(2\mathrm{x}+3\right)-1\left(2\mathrm{x}+3\right) \\ =\left(3\mathrm{x}-1\right)\left(2\mathrm{x}+3\right) \\ \left(\mathrm{ii}\right). \\ 84-2\mathrm{r}-2{\mathrm{r}}^2 \\ =-2{\mathrm{r}}^2-2\mathrm{r}+84 \\ =-2\left[{\mathrm{r}}^2+\mathrm{r}-42\right] \\ =-2\left[{\mathrm{r}}^2+7\mathrm{r}-6\mathrm{r}-42\right] \\ =-2\left[\mathrm{r}\left(\mathrm{r}+7\right)-6\left(\mathrm{r}+7\right)\right] \\ =-2\left(\mathrm{r}-6\right)\left(\mathrm{r}+7\right) \end{gathered}$$