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When a polynomial p(x) of degree 3 is di...

When a polynomial `p(x)` of degree 3 is divided by `3x^2-8x+5` quotient and remainder obtained are linear polynomial such that `p(1)=19` and `p(5/3)=25`. So,find the remainder polynomial.

Text Solution

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`f(x)=(3x^2-8x+5)(ax+b)+(cx+d)`
put x=1
`P(1)=(3*1-8+5)(a+b)+c+d=19`
`c+d=19-(1)`
Put x=5/3
`p(5/3)=(3*25/8-8*5/3+5)(a*5/3+b)(c*5/3+d)=25`
`(-5+5)(5/3a+b)+(5/3c+d)=25`
`5/3c+d=25`
...
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