1.

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`.

Answer» `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)`
put x=-2
`p(-2)=(4+6+2)(4a-2b+1)=132`
`12(4a-2b+1)=132`
`2a-b=5-(2)`
subtracting equation 1 from equation 2
`a=2`
`b=-1`
`P(x)=(x^2-3x+2)(ax^2+bx+c)`
`P(x)=(x^2-3x+2)(2x^2-x+1)`.


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