Divide  
(
5
x
7
−
15
x
3
+
6
x
2
)
  by  
(
5
x
2
)
 .

We need to divide the expression:

\[
(5x^7 - 15x^3 + 6x^2) \quad \text{by} \quad (5x^2).
\]

Let's break it down by dividing each term of the numerator by the denominator:

\[
\frac{5x^7}{5x^2} = x^{7-2} = x^5,
\]
\[
\frac{-15x^3}{5x^2} = -\frac{15}{5}x^{3-2} = -3x,
\]
\[
\frac{6x^2}{5x^2} = \frac{6}{5}.
\]

So, the final result is:

\[
x^5 - 3x + \frac{6}{5}.
\]

### Final Answer:
\[
x^5 - 3x + \frac{6}{5}.
\]

Would you like more details or have any questions?

Here are five related questions:
1. How do you simplify expressions with exponents when dividing?
2. How do you handle polynomials when dividing by a monomial?
3. Can you explain the difference between dividing and factoring polynomials?
4. What happens when the numerator has terms of lower degree than the denominator?
5. How do you perform polynomial long division?

**Tip:** When dividing terms with exponents, subtract the exponents of the same base.

This guide explains how to divide the polynomial (5x^7 - 15x^3 + 6x^2) by (5x^2) using algebraic rules and exponent laws. The step-by-step solution simplifies the polynomial, breaking it down term by term. Ideal for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation