Question

Factorise the expressions and divide them as directed:

1. (4 p²- 20 p + 16)÷ (p - 1).
2. 39 y³(50 y²- 98)÷ 26 y²(5 y + 7).
3. (m^{2 +}7 m + 10)÷ (m + 5)

Answer 1

$$\begin{gathered} \left(1\right). \\ \frac{4{\mathrm{p}}^2-20\mathrm{p}+16}{\mathrm{p}-1} \\ =\frac{4\left({\mathrm{p}}^2-5\mathrm{p}+4\right)}{\left(\mathrm{p}-1\right)} \\ =\frac{4\left({\mathrm{p}}^2-4\mathrm{p}-\mathrm{p}+4\right)}{\left(\mathrm{p}-1\right)} \\ =\frac{4\left[\mathrm{p}\left(\mathrm{p}-4\right)-1\left(\mathrm{p}-4\right)\right]}{\left(\mathrm{p}-1\right)} \\ =\frac{4\left(\mathrm{p}-1\right)\left(\mathrm{p}-4\right)}{\left(\mathrm{p}-1\right)} \\ =4\left(\mathrm{p}-4\right) \\ \left(2\right). \\ \frac{39{\mathrm{y}}^3\left[50{\mathrm{y}}^2-98\right]}{26{\mathrm{y}}^2\left(5\mathrm{y}+7\right)} \\ =\frac{78{\mathrm{y}}^3\left[25{\mathrm{y}}^2-49\right]}{26{\mathrm{y}}^2\left(5\mathrm{y}+7\right)} \\ =\frac{3\mathrm{y}\left[{\left(5\mathrm{y}\right)}^2-{\left(7\right)}^2\right]}{\left(5\mathrm{y}+7\right)} \\ =\frac{3\mathrm{y}\left(5\mathrm{y}+7\right)\left(5\mathrm{y}-7\right)}{\left(5\mathrm{y}+7\right)} \\ =3\mathrm{y}\left(5\mathrm{y}-7\right) \\ \left(3\right). \\ \frac{{\mathrm{m}}^2+7\mathrm{m}+10}{\mathrm{m}+5} \\ =\frac{{\mathrm{m}}^2+5\mathrm{m}+2\mathrm{m}+10}{\mathrm{m}+5} \\ =\frac{\mathrm{m}\left(\mathrm{m}+5\right)+2\left(\mathrm{m}+5\right)}{\mathrm{m}+5} \\ =\frac{\left(\mathrm{m}+5\right)\left(\mathrm{m}+2\right)}{\left(\mathrm{m}+5\right)} \\ =\mathrm{m}+2 \end{gathered}$$