Question

Factorise the following expressions

(i) p² + 6p + 8

(ii) q² − 10q + 21

(iii) p² + 6p − 16

Answer 1

(i) p² + 6p + 8

It can be observed that, 8 = 4 × 2 and 4 + 2 = 6

∴ p² + 6p + 8 = p² + 2p + 4p + 8

= p(p + 2) + 4(p + 2)

= (p + 2) (p + 4)

(ii) q² − 10q + 21

It can be observed that, 21 = (−7) × (−3) and (−7) + (−3) = − 10

∴ q² − 10q + 21 = q² − 7q − 3q + 21

= q(q − 7) − 3(q − 7)

= (q − 7) (q − 3)

(iii) p² + 6p − 16

It can be observed that, 16 = (−2) × 8 and 8 + (−2) = 6

p² + 6p − 16 = p² + 8p − 2p − 16

= p(p + 8) − 2(p + 8)

= (p + 8) (p − 2)
​​​​​​​​​​​​​​​​​​​​​