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Factorisation

Short Answer Type

101.

Factorise the expression and divide them as directed.

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

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102.

Factorise the expression and divide them as directed.

(5p² - 25p + 20) $divided by$ (p - 1)

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103.
Factorise the expressions and divide them as directed.

4yz(z² + 6z - 16) $divided by$ 2y(z + 8)

∵             z² + 6z -16 = z² + 8z - 2z - 16               ∵ 8 - 2 = 6

                               = z(z + 8) - 2(z + 8)        ∵ 8 × 2 = 16

                               = (z + 8)(z - 2)

∴ $fraction numerator 4 yz left parenthesis straight z squared plus 6 straight z minus 16 right parenthesis over denominator 2 straight y left parenthesis straight z plus 8 right parenthesis end fraction space equals space fraction numerator 2 cross times 2 cross times straight y cross times straight z cross times left parenthesis straight z plus 8 right parenthesis cross times left parenthesis straight z minus 2 right parenthesis over denominator 2 cross times straight y cross times left parenthesis straight z plus 8 right parenthesis end fraction$

 = $fraction numerator 2 cross times straight z cross times left parenthesis straight z plus 2 right parenthesis over denominator 1 end fraction space equals space 2 straight z left parenthesis straight z minus 2 right parenthesis$

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