1.

Determine which of the following polynomial has x-2 a factor (i) `3x^(2)+6x-24` (ii) `4x^(2)+x-2`

Answer» (i) let `p(X) =3x^(2)+6x-24`
On putting x=2 in Eq (i) We get
`p(2)=3(2)^(2)+6(2)-24`
`=3xx4+12-24=12-12=0`
hence ,x-2 is a factor of p(x) .
(ii) Let p(x) `=4x^(2)+x-2`
On putting x=2 in Eq (i) we get
`p(2)=2(2)^(2)+2-2=4xx4+0`
`16=16ne 0`
hence ,x-2 is not a factor of p(x).


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