(-2x^2-7x+1) divided by (x^2+3) long division

Let's perform the long division of the polynomial \(-2x^2 - 7x + 1\) by \(x^2 + 3\).

### Step 1: Set Up the Division

We divide the terms of the dividend \((-2x^2 - 7x + 1)\) by the leading term of the divisor \((x^2 + 3)\).

\[
\frac{-2x^2 - 7x + 1}{x^2 + 3}
\]

### Step 2: Divide the Leading Terms

Divide the leading term of the dividend \(-2x^2\) by the leading term of the divisor \(x^2\):

\[
\frac{-2x^2}{x^2} = -2
\]

### Step 3: Multiply and Subtract

Multiply the entire divisor \(x^2 + 3\) by \(-2\):

\[
-2 \cdot (x^2 + 3) = -2x^2 - 6
\]

Subtract this product from the original dividend:

\[
(-2x^2 - 7x + 1) - (-2x^2 - 6) = -7x + 7
\]

### Step 4: Divide the New Leading Term

Now divide the new leading term \(-7x\) by the leading term of the divisor \(x^2\):

\[
\frac{-7x}{x^2} = 0
\]

Since this term does not contribute further to the quotient, we stop here.

### Final Quotient and Remainder

The quotient is:

\[
-2
\]

The remainder is:

\[
-7x + 7
\]

Thus, the final answer is:

\[
\frac{-2x^2 - 7x + 1}{x^2 + 3} = -2 + \frac{-7x + 7}{x^2 + 3}
\]

Would you like further details or have any questions?

### Related Questions

1. How would the remainder change if the divisor was \(x^2 - 3\)?
2. What is the long division process when the divisor is of higher degree than the dividend?
3. How can the remainder be expressed as a simpler form of fractions?
4. What happens if the coefficients of the terms were complex numbers?
5. How would you perform synthetic division on polynomials?

**Tip:** Always ensure that you align terms correctly in long division to avoid mistakes during subtraction.

(-2x^2 - 7x + 1) divided by (x^2 + 3) long division

Learn how to perform long division of the polynomial (-2x^2 - 7x + 1) by (x^2 + 3) with a detailed step-by-step solution. This problem covers important algebraic concepts in polynomial division, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation