Question

Polynomial are given:P


`p |x | = {x}^(3) - 3 {x}^(2) + 2x - 1`
show if

`x = 1`
is the root of the polynomial.


Erpress the polynomial

`p |x|`
in the tratment

`p |x| = (x - 1)( {x}^(2) + ax + b) + c`

Answer 1

• x = 1 is not a root
• p(x) = (x -1)(x^2 -2x +0) -1

Explanation:

a) p(1) = 1³ -3·1² +2·1 -1 = 1 -3 +2 -1 = -1 . . . . not zero

b) Dividing p(x) by x-1 gives x² -2x +0 with a remainder of -1 (as found in part (a)). So the function can be written as ...

... p(x) = (x -1)(x² -2x +0) -1

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Polynomial division can be done using synthetic division or long division. The latter can be done by hand or by using any of several on-line calculators. Attached is output from one of them.