Question

Factorise the followingexpressions

(i) p²+ 6p + 8

(ii) q²− 10q + 21

(iii) p²+ 6p − 16

Answer 1

(i) p²+ 6p + 8

Itcan 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

Itcan 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

Itcan 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)