Question

Divide using factorisation
$({m}^{2} - 14m - 32) \div (m + 2)$
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Answer 1

$\large\sf\underline{Given\::}$

• $\sf\:\frac{m^{2}-14m-32}{(m+2) }$

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$\large\sf\underline{To\::}$

• Divide the given expression

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$\large\sf\underline{Solution\::}$

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$\sf\:\frac{m^{2}-14m-32}{(m+2) }$

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• Let's factorise the numerator by middle term breaking

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So for factorising we need such two terms whose product gives us 32 and whose sum or difference would give us middle term ( 14 ) .

That two terms would be 16 and 2 .

• 16 × 2 = 32

• 16 - 2 = 14

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Now substituting the two terms in the expression :

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$\sf\longrightarrow\:\frac{m^{2}-(16-2)m-32}{(m+2) }$

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• Multiplying the terms in numerator

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$\sf\longrightarrow\:\frac{m^{2}-16m+2m-32}{(m+2) }$

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• Taking m from first two terms and 2 from second two terms as common in numerator

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$\sf\longrightarrow\:\frac{m(m-16)+2(m-16)}{(m+2) }$

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• Taking ( m - 16 ) common from whole terms in numerator

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$\sf\longrightarrow\:\frac{(m-16)(m+2)}{(m+2) }$

$\sf\longrightarrow\:\frac{(m-16)\cancel{(m+2)}}{\cancel{(m+2)}}$

$\small\fbox\red{★\:(\:m\:-\:16\:)}$

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!! Hope it helps !!