SOLUTION: factor f(x) into linear factors given that k is a zero of f(x) f(x)= x^4+3x^3-30x^2-124x-120;k=-2 (multiplicity 2)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: factor f(x) into linear factors given that k is a zero of f(x) f(x)= x^4+3x^3-30x^2-124x-120;k=-2 (multiplicity 2)      Log On


   

Question 1113975: factor f(x) into linear factors given that k is a zero of f(x)
f(x)= x^4+3x^3-30x^2-124x-120;k=-2 (multiplicity 2)
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
-2   |   1   3   -30   -124   -120
     |       -2  -2    64      120
     |-------------------------------
        1   1    -32   -60     0


Next, break into factors for x%5E3%2Bx%5E2-32x-60.
You know there is another root of -2 because given was "multiplicity 2".

Synthetic division on the above dividend will give quotient x%5E2-x-30 and the two previous factors were x%2B2 and x%2B2.

Factorization of x%5E2-x-30 is easily done:
%28x%2B5%29%28x-6%29


Entire factorization is then %28x%2B2%29%5E2%2A%28x%2B5%29%28x-6%29.