Question

Factorise the expressions and divide them as directed. (i) `(y^2+7y+10) -: (y+5)` (ii) `(m^2-14m-32) -: (m+2)` (iii) `(5p^2-25p+20) -: (p-1)` (iv) `(4yz(z^2+6z-16) -: 2y (z+8)` (v) `5pq(p^2-q^2) -: 2p(p+q)` (vi) `12xy (9x62-16y^2) -: 4xy (3x+4y)` (vii) `39y^3(50y^2-98) -: 26y^2(5y+7)`

Answer 1

(i)` (y^2+7y+10)/(y+5)`
`=(y^2+5y+2y+10)/(y+5)`
`=(y(y+5)+2(y+5))/(y+5)`
`=((y+5)(y+2))/(y+5)`
`=y+2.`
(v)` (5pq(p^2-q^2))/(2p(p+q))`
`= (5pq(p+q)(p-q))/(2p(p+q))`
`=(5q(p-q))/2`
(vii) `(39y^3(50y^2-98))/(26y^2(5y+7))`
`= (39y^3*2(25y^2-49))/(26y^2(5y+7))`
`= (39y^3*2((5y)^2-7^2))/(26y^2(5y+7))`
`= (39y^3*2(5y+7)(5y-7))/(26y^2(5y+7))`
`=3y(5y-7).`
Similarly, we can solve the remaining parts.