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Factorisation

Short Answer Type

101.
Factorise the expression and divide them as directed.

$left parenthesis straight m squared space minus space 14 straight m space minus space 32 right parenthesis space divided by space left parenthesis straight m space plus space 2 right parenthesis$

∵ m² -14m - 32 = (m² - 16m + 2m - 32] [∵ -14 = -16 + 2]

= m(m - 16) + 2(m - 16) [16 × 2 = 32]

= (m - 16)(m + 2)

∴ $fraction numerator straight m squared minus 14 straight m minus 32 over denominator straight m plus 32 end fraction equals fraction numerator left parenthesis straight m minus 16 right parenthesis left parenthesis straight m plus 2 right parenthesis over denominator left parenthesis straight m plus 2 right parenthesis end fraction equals fraction numerator straight m minus 16 over denominator 1 end fraction$

Thus, $left parenthesis straight m squared space minus space 14 straight m space minus space 32 right parenthesis space divided by space left parenthesis straight m space plus space 2 right parenthesis space equals straight m space minus 16$