Determine if x + 3 is a factor of -3x^(3)+6x^(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,…

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

Option C

no, because the remainder is 126

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.