Question

Q- Factorise by splitting the middle term:

(a) p²+2p-15

(b) m²-3m-70

(c) 3x²-10x+8

Answer 1

$$\begin{gathered} \left(\mathbf{1}\right)\mathbf{.} \\ {p}^2+2p-15 \\ =p^2+5p-3p-15 \\ =p\left(p+5\right)-3\left(p+5\right) \\ =\left(p-3\right)\left(p+5\right) \\ \left(\mathbf{2}\right)\mathbf{.} \\ {m}^2-3m-70 \\ =m^2-10m+7m-70 \\ =m\left(m-10\right)+7\left(m-10\right) \\ =\left(m+7\right)\left(m-10\right) \\ \left(\mathbf{3}\right)\mathbf{.} \\ 3x^2-10x+8 \\ =3x^2-6x-4x+8 \\ =3x\left(x-2\right)-4\left(x-2\right) \\ =\left(3x-4\right)\left(x-2\right) \end{gathered}$$