Question

Determine if x + 3 is a factor of -3x^3+6x^2+6x+9 How do you know

Answer 1

Answer:

  x+3 is not a factor

Step-by-step explanation:

A graphing calculator shows the expression has a zero at x=3 and no other real zeros. If x+3 were a factor, there would be a zero at x = -3.

  x+3 is not a factor of the expression.

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You can check to see if x+3 is a factor by evaluating the expression for x=-3. If (x+3) is a factor, x=-3 will make the function be zero.

  3(-x³ +2x² +2x +3) = 3(((-x +2)x +2)x +3) = 3(((-(-3)+2)(-3) +2)(-3) +3)

  = 3((-15+2)(-3) +3) = 3(39 +3) = 126 ≠ 0

The expression evaluates to 126 at x=-3, so x+3 is NOT a factor.