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Check whether (2x-3) is a factor of the ...

Check whether (2x-3) is a factor of the polynomial `2x^(4)+9x^(2)-11x-30` ?

Text Solution

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Let 2x-3=0
`implies 2x=3`
`implies x=(3)/(2)`
Let `p(x)=2x^(4)+9x^(2)-11x-30`
`implies p((3)/(2))=2((3)/(2))^(4)+9((3)/(2))^(2)-11((3)/(2))-30=(81)/(8)+((81)/(4)-(33)/(2))-30`
`=(81+162-132-240)/(8)=-(129)/(8)`
` because` Remainder is not equal to zero.
`therefore` 2x-3, is not a factor of given polynomial.
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