SOLUTION: One of the zeros of the polynomial function is 5. {{{ f(x) = x^4 - 4x^3 - 21x^2 + 100x - 100 }}} What is the factored form of the function? The equation is in the link her

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: One of the zeros of the polynomial function is 5. {{{ f(x) = x^4 - 4x^3 - 21x^2 + 100x - 100 }}} What is the factored form of the function? The equation is in the link her      Log On


   

Question 1127904: One of the zeros of the polynomial function is 5.
+f%28x%29+=+x%5E4+-+4x%5E3+-+21x%5E2+%2B+100x+-+100+
What is the factored form of the function?
The equation is in the link here: https://prnt.sc/lduhcc
Is my answer correct?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
------
One of the zeros of the polynomial function is 5.
+f%28x%29+=+x%5E4+-+4x%5E3+-+21x%5E2+%2B+100x+-+100+
What is the factored form of the function?
The equation is in the link here: https://prnt.sc/lduhcc
Is my answer correct?
------ 

5    |    1    -4    -21    100    -100
     |
     |          5      5    -80     100
     |_______________________________________
          1     1     -16    20      0



2    |    1    1    -16    20
     |         2     6    -26
     ______________________________
         1     3    -13     -6


-2   |   1   1   -16   20
     |      -2     2   28
     |________________________
         1  -1    -14  48


5    |      1     1     -16    20
     |
     |            5     30
     |_________________________________
            1     6     14     nonzero


2    |    1    1    -16    20
     |         2       6   -20
     |______________________________
          1    3     -10    0

        x%5E2%2B3x-10=%28x-2%29%28x%2B5%29

Complete Factorization for f(x) is
%28x-2%29%28x-2%29%28x%2B5%29%28x-5%29
OR
%28x%2B5%29%28x-5%29%28x-2%29%5E2

Answer by ikleyn(52905) About Me  (Show Source):
You can put this solution on YOUR website!
.

See my plot below, which confirms your answer.





Plot y = x%5E4+-+4x%5E3+-+21x%5E2+%2B+100x+-+100


Making the plot is the most powerful and quick method to see the roots,


at least to create a hypotheses, which should be checked later by numerical calculations or/and algebraic proofs.