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Without actual division, prove that 2x^4...

Without actual division, prove that `2x^4-5x^3+2x^2-x+2` is exactly divisible by `x^2-3x+2.`

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`p(x)=2x^4−5x^3+2x^2−x+2`
and `x^2−3x+2=(x−1)(x−2)`
Let `x^2−3x+2` is the factor of `p(x)`
Then,
`x^2−3x+2=0`
`⇒(x−1)(x−2)=0`
`⇒x=1` and `x=2`
For `x=1`
`P(1)=0`
and For `x=2`
`p(2)=0`
`∵p(1)=p(2)=0`
`∴p(x)` is divisible by `x^2−3x+2`
Hence proved.
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  20. For what value of a is (x-5) a factor of x^3-3x^2+a x-10 ?

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