To divide the polynomial [tex]\( 30x^2 + 5x - 2 \)[/tex] by the monomial [tex]\(-5x\)[/tex], we need to perform the division term-by-term. Here’s a detailed step-by-step solution:
1. Divide each term in the polynomial by the monomial:
[tex]\[
\frac{30x^2}{-5x} + \frac{5x}{-5x} + \frac{-2}{-5x}
\][/tex]
2. Simplify each term individually:
- For the first term:
[tex]\[
\frac{30x^2}{-5x} = \frac{30}{-5} \cdot \frac{x^2}{x} = -6x
\][/tex]
- For the second term:
[tex]\[
\frac{5x}{-5x} = \frac{5}{-5} \cdot \frac{x}{x} = -1
\][/tex]
- For the third term:
[tex]\[
\frac{-2}{-5x} = -\left(\frac{2}{5x}\right) = 0.4 \cdot \frac{1}{x} = 0.4/x
\][/tex]
3. Combine the simplified terms:
[tex]\[
-6x - 1 + \frac{0.4}{x}
\][/tex]
Thus, the simplified form of the polynomial divided by the monomial is:
[tex]\[
-6x - 1 + \frac{0.4}{x}
\][/tex]
