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If the polynomial ax^(3)+3x^(2)-3 leaves...

If the polynomial `ax^(3)+3x^(2)-3` leaves the remainder 6 when divided by x-4, then find the value of a.

Text Solution

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Let x-4=0
`implies x=4`
Let `p(x)=ax^(3)+3x^(2)-3`
Given that p(4)=6
`implies a(4)^(3)+3(4)^(2)-3=6`
`implies 64a+48-3=6`
`implies 64a=6+3-48=-39`
`implies a=(-39)/(64)`
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