Question

Which of the following correctly divides 18x2+9x+3 by −3x ?(1 point) Responses −6x−9−3x negative 6 x minus 9 minus Start Fraction 3 over x End Fraction 6x+3+1x 6 x plus 3 plus Start Fraction 1 over x End Fraction −6x−3−1x negative 6 x minus 3 minus Start Fraction 1 over x End Fraction −15x−3

Answer 1

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

1. Divide \(18x^2\) by \(-3x\): \[ \frac{18x^2}{-3x} = -6x \]

2. Divide \(9x\) by \(-3x\): \[ \frac{9x}{-3x} = -3 \]

3. Divide \(3\) by \(-3x\): \[ \frac{3}{-3x} = -\frac{1}{x} \]

Now, we combine these results together: \[ \text{Result} = -6x - 3 - \frac{1}{x} \]

Thus, the expression resulting from the division \( \frac{18x^2 + 9x + 3}{-3x} \) is: \[ -6x - 3 - \frac{1}{x} \]

So, the correct response is: \[ -6x - 3 - \frac{1}{x} \]