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Find a polynomial p(x) of degree 4, whic...

Find a polynomial `p(x)` of degree 4, which has `x^2-3x+2` as a factor and also given that `p(-1)=24,p(-2)=132` and ` p(0)=2`.

Text Solution

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`p(x)=(x^2-3x+2)(ax^2+bx+c)`
put x=0
`P(0)=2c=2`
`c=1`
put x=-1
`p(-1)=(1+3+2)(a-b+1)=24`
`6(a-b+1)=24`
`a-b=3-(1)`
...
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