SOLUTION: Show that the number is a zero of f(x) of the given multiplicity and express f(x) as a product of linear factors: f(x)=x^4-9x^3+22x^2-32; 4(multi. 2)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Show that the number is a zero of f(x) of the given multiplicity and express f(x) as a product of linear factors: f(x)=x^4-9x^3+22x^2-32; 4(multi. 2)      Log On


   

Question 1051363: Show that the number is a zero of f(x) of the given multiplicity and express f(x) as a product of linear factors: f(x)=x^4-9x^3+22x^2-32; 4(multi. 2)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The zeros possible would be the plusses and minuses of 2, 4, 8, 16, 32. Only expect no more than three of these to be the zeros.

You are interested in zero or root of with the value 4. Perform successive synthetic divisions starting with f(x) until the remainder is nonzero. THAT is what to do. That will show the multiplicity ---- how many of these synthetic successive divisions gave remainder of 0? 

Do you understand why the 0 is included in the dividend here?


4     |      1   -9   22    0    -32
      |
      |           4   -20   8     32
      |_____________________________________
            1    -5   2     8      0

The new dividend is now the quotient from this finished division.


4    |     1    -5    2    8
     |
     |          4    -4    -8
     |_____________________________
          1      -1  -2    0

You can understand here than no further synthetic division testing 4 as root will give a remainder of 0; so this checking is finished.