Which of the following correctly divides 18x2+9x+3

18
𝑥
2
+
9
𝑥
+
3
by −3x

3
𝑥
?(1 point)
Responses

6x+3+1x
6
𝑥
+
3
+
1
𝑥
6 x plus 3 plus Start Fraction 1 over x End Fraction

−15x−3

15
𝑥

3
negative 15 x minus 3

−6x−3−1x

6
𝑥

3

1
𝑥
negative 6 x minus 3 minus Start Fraction 1 over x End Fraction

−6x−9−3x

1 answer

To divide the polynomial \( 18x^2 + 9x + 3 \) by \( -3x \), we can perform polynomial long division or simply divide each term of the polynomial by \( -3x \).

Let's divide each term of \( 18x^2 + 9x + 3 \) by \( -3x \):

  1. \( \frac{18x^2}{-3x} = -6x \)
  2. \( \frac{9x}{-3x} = -3 \)
  3. \( \frac{3}{-3x} = -\frac{1}{x} \)

Putting it all together, we get:

\[ \frac{18x^2 + 9x + 3}{-3x} = -6x - 3 - \frac{1}{x} \]

Therefore, the correct response from the options provided is:

\(-6x - 3 - \frac{1}{x}\) (which corresponds to "−6x−3−1x").