Question

Factorise the following expressions 

1. \(p^ 2 + 6p + 8\) 
2.  \(q^ 2 - 10q + 21\) 
3.  \(p^ 2 + 6p - 16\)

Answer 1

(i) \(p^2+ 6p + 8\)
It can be observed that, \(8 = 4 \times 2\) and \(4 + 2 = 6\)
∴ \(p^2+ 6p + 8 = p^2+ 2p + 4p + 8\)
= \(p(p + 2) + 4(p + 2)\)
= \((p + 2) (p + 4)\)

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(ii) \(q^2- 10q + 21\)
It can be observed that, \(21 = (-7) \times (-3)\) and \((-7) + (-3) = - 10\)
∴ \(q^2- 10q + 21 = q^2- 7q - 3q + 21\)
= \(q(q - 7) - 3(q - 7)\)
= \((q - 7) (q - 3)\)

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(iii) \(p^2+ 6p - 16\)
It can be observed that, \(16 = (-2) \times 8\) and \(8 + (-2) = 6\)
\(p^2+ 6p - 16 = p^2+ 8p - 2p - 16\)
= \(p(p + 8) - 2(p + 8)\)
= \((p + 8) (p - 2)\)