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Factorisation by Common Factors

Factorise the...

Question

Factorise the expression $m^{2} - 4 m - 21$

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Solution

Comaring $m^{2} - 4 m - 21$ with the identity $x^{2} + (a + b) x + a b$ we not that ab = - 21, and a + b = - 4. So, (-7) + 3 = 4 and (-7)(3) = -21
Hence, $m^{2} - 4 m - 21 = m^{2} - 7 m + 3 m - 21$
$= m (m - 7) + 3 (m - 7)$
$= (m - 7) (m + 3)$
Therefore $m^{2} - 4 m - 21 = (m - 7) (m + 3)$

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