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For all y ne 5, (y^(3)-6y^(2)+3y+10)/(y^(2)-10y+25)=

Answer»

`(y^(2)-y+2)/(y+5)`
`(y^(2)-y-2)/(y-5)`
`(y^(2)+y-2)/(y+5)`
`(y^(2)+y-2)/(y-5)`

Solution :Since the DENOMINATOR has a lower POWER, factor that expression first.
`y^(2)-10 y + 25 = (y-5)(y-5)`
Cheq each numerator in the answer options to determine which polynomial gives a PRODUCT of `y^(3)-6y^(2)+3y+10` when multiplied by `(y-5). Y^(3)-6y^(2)+3y+10 = (y-5)(y^(2)-y-2)`.
Then `(y^(3)-6y^(2)+3y+10)/(y^(2)-10y+25)=((y-5)(y^(2)-y-2))/((y-5)(y-5))`
`= (y^(2)-y-2)/(y-5)`.


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