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Polynomials, SMB-005

Consider the polynomial  `P(x) = x^3-4x^2+x+6`.

  1. Show that  `x = -1`  is a zero of  `P(x)`.  (1 mark)

  2. Find the other zeros.  (2 marks)

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  1. `text(See Worked Solution)`
  2. `x = 2 and 3`
Show Worked Solution

i.   `P(-1) = -1-4-1+6 = 0`

`:. x=-1\ \ text(is a zero)`

 

ii.   `text{Using part (i)} \ => (x+1)\ text{is a factor of}\ P(x)`

`P(x) = (x+1)*Q(x)`
 

`text(By long division:)`

`P(x)` `= (x+1) (x^2-5x+6)`
  `= (x+1)(x-2)(x-3)`

 
`:.\ text(Other zeroes are:)`

`x = 2 and x = 3`