Question

Determine if x + 3 is a factor of -3$x^{3}$+6$x^{2}$+6x+9. How do you know?

no, because the remainder is 126

yes, because the remainder is 126

no, because the remainder is –108

yes, because the remainder is –108

Answer 1

Answer:

Option C

no, because the remainder is 126

Step-by-step explanation:

Given the polynomial equation in the question

-3x^{3}+6x^{2}+6x+9

factor =  x + 3 (divisor)

long division

          -3x² + 15x - 39             Quotient

          --------------------------------

x + 3|  -3x³ + 6x² + 6x + 9     Dividend

        |  -3x³ - 9x²

                   ----------------------

                      15x² + 6x + 9

                      15x² + 45x

                      --------------------

                               -39x + 9

                               -39x - 117

                                 -------------

                                           126   Reminder

Since reminder is not zero so (x + 3) is not factor of -3x³ + 6x² + 6x + 9.

(x-3) is the factor of  -3x³ + 6x² + 6x + 9.