Question

divide by factorising the expression [m^2-2m-63]÷[m+7]​

Answer 1

m+7 ÷ m2 - 2m - 63.

m2 +7m.
( - ). ( - ).

-9m - 63
-9m -63

0

q(x) = m - 9 = answer

Answer 2

$[m^2 - 2m - 63 ] \div [m + 7] = m - 9$

Solution:

Given that,

We have to divide by factorising the expression

$[m^2 - 2m - 63 ] \div [m + 7]$

Let us solve by factorising the expression

$\frac{m^2 - 2m - 63 } {m + 7}$

Factorize the numerator

$m^2-2m-63\\\\Split\ the\ middle\ term\\\\m^2 + 7m -9m - 63\\\\\mathrm{Break\:the\:expression\:into\:groups}\\\\\left(m^2+7m\right)+\left(-9m-63\right)\\\\\mathrm{Factor\:out\:}m\mathrm{\:from\:}\m^2+7m \\\\m(m + 7) + (-9m - 63)\\\\\mathrm{Factor\:out\:}-9\mathrm{\:from\:}-9m-63\mathrm{:\quad }\\\\m\left(m+7\right)-9\left(m+7\right)\\\\\mathrm{Factor\:out\:common\:term\:}m+7\\\\\left(m+7\right)\left(m-9\right)$

Thus the expression becomes:

$\frac{m^2 - 2m - 63 } {m + 7} = \frac{ (m+7)(m-9)}{m+7}\\\\\frac{m^2 - 2m - 63 } {m + 7} = m-9$

Thus the result is m - 9

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