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Factorize 42-r-r^2....

Factorize `42-r-r^2`.

Text Solution

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The given expression may be written as `-r^2-r+42`.
Here, `(-1)xx 42 =-42`.
So, we split -1 into two parts whsoe sum is `-1` and product `-42`.
Clearly , `(-7)+6=-1 and (-7)xx6=-42`.
`therefore 42-r-r^2=-r^2-r+42`
`=-r^2-7r+6r+42`
`=-r(r+7)+6(r+7)`
`=(r+7)(-r+6)=(7+r) (6-r)`.
Hence, `(42-r-r^2)=(7+r)(6-r)`.
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