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Which statements are true about the polynomial function?

f(x)=x^3−x^2−4x+4

Select each correct answer. Please explain your answer.


f(x)=0 when x=−1 .

f(x) divided by (x−1) has a remainder of 0.

(x−1) is a factor of f(x) .

f(−1)=0

Respuesta :

altavistard
Is "f(x)=0 when x=−1" true or not?  To answer this, use synth. div. with -1 as the divisor.  Is the remainder 0?  If yes, then -1 is a root and f(-1) = 0.

Setting up synth. div.:
      ______________
-1  /   1   -1   -4   4
              -1    2   2
     ------------------------
         1   -2    -2   6     The remainder is 6, so -1 is not a root, and f(x) does
                                   not equal 0 when x = -1.


"f(x) divided by (x−1) has a remainder of 0."  Again, set up synth. div., this time with divisor +1:

1   /   1   -1   -4   4
               1   0    -4
     ------------------------
         1    0    -4   0     The remainder is 0, so 1 is a root and x-1 is a 
                                   factor.
                                 
avigo4264

Answer:

f(x)  divided by (x−1)  has a remainder of 0.

(x−1)  is a factor of  f(x) .

Step-by-step explanation:

complete test attached

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