Question

Factorise and divide the expressions given

i.) $(m^2-11m-42)÷(m+3)$

ii.) $39y^3(50y^2-98)÷26y^2(5y+7)$ [4 MARKS]

Answer 1

Application: 2 Marks each

(i) $m^2-11m-42=m^2-14m+3m-42=m(m-14)+3(m-14)=(m+3)(m-14)$

$\frac{m^2-11m-42}{(m+3)}=m-14$


(ii) $39y^3(50y^2-98)=3\times 13\times y\times y\times y\times 2\left[\right(25y^2-49\left)\right]$

$=3\times 13\times 2\times y\times y\times y\times \left[\right(5y{)}^2-\left(7{)}^2\right]$

$=3\times 13\times 2\times y\times y\times y(5y-7)(5y+7)$

$26y^2(5y+7)=2\times 13\times y\times y\times (5y+7)$

$39y^3(50y^2-98)÷26y^2(5y+7)$

$=\frac{39y^3\times 2(25y^2-49)}{26y^2(5y+7)}$

$=\frac{3y(5y+7)(5y-7)}{(5y+7)}$

$=3y(5y-7)$