ulo IsDe Uy ( 5). Without actual division, show that (x - 3x2 - 13x +15) is exactly divisible by (x² + 2x - 3).

$$\begin{gathered} let f\left(\pi \right)=x^3-3x^2-13x+15 \\ divisible by x^2+2x-3 \\ (x+3)(x-1) \\ by remainder theorem \\ r=0 \\ So, x=-3 \\ \Rightarrow f(-3)=-27-27+39+15 \\ =0 \\ f\left(1\right)=1-3-13+15 \\ =16-16=0 \\ \mathit{W}\mathit{e}\mathbf{ }\mathit{c}\mathit{a}\mathit{n}\mathbf{ }\mathit{s}\mathit{a}\mathit{y}\mathbf{ }\mathit{t}\mathit{h}\mathit{a}\mathit{t}\mathbf{ }\mathit{t}\mathit{h}\mathit{e}\mathbf{ }\mathit{g}\mathit{i}\mathit{v}\mathit{e}\mathit{n}\mathbf{ }\mathit{e}\mathit{q}\mathit{n}\mathbf{.}\mathbf{ }\mathit{i}\mathit{s}\mathbf{ }\mathit{d}\mathit{i}\mathit{v}\mathit{i}\mathit{s}\mathit{i}\mathit{b}\mathit{l}\mathit{e}\mathbf{ }\mathit{b}\mathit{y}\mathbf{ }{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathit{x}\mathbf{-}\mathbf{3} \\ \mathit{H}\mathit{e}\mathit{n}\mathit{c}\mathit{e}\mathbf{,}\mathbf{ }\mathit{p}\mathit{r}\mathit{o}\mathit{v}\mathit{e}\mathit{d} \end{gathered}$$