Question

Divide each polynomial expression by the monomial expression
8x^2 + 8x / 2x
-21x^2 + 96x - 15 / 3
-36x^6 + 96x^4 / 3x^2

Answer 1

Let's divide each polynomial expression by the given monomial expression:

1. **For \( \frac{8x^2 + 8x}{2x} \)**:
\[
\frac{8x^2}{2x} + \frac{8x}{2x} = \frac{8}{2}x^{2-1} + \frac{8}{2}x^{1-1}
\]
This simplifies to:
\[
4x + 4
\]

2. **For \( \frac{-21x^2 + 96x - 15}{3} \)**:
\[
\frac{-21x^2}{3} + \frac{96x}{3} - \frac{15}{3} = -7x^2 + 32x - 5
\]

3. **For \( \frac{-36x^6 + 96x^4}{3x^2} \)**:
\[
\frac{-36x^6}{3x^2} + \frac{96x^4}{3x^2} = \frac{-36}{3} x^{6-2} + \frac{96}{3} x^{4-2}
\]
This simplifies to:
\[
-12x^4 + 32x^2
\]

In summary, the results of the divisions are:

1. \( 4x + 4 \)
2. \( -7x^2 + 32x - 5 \)
3. \( -12x^4 + 32x^2 \)