Divide the expression x³ + 7x² - x - 7 by -1 + x²

Memememememememememememememe

1 year ago

Let's divide **\( x^3 + 7x^2 - x - 7 \)** by **\( x^2 - 1 \)** using polynomial long division.

### Step 1: Divide the first term
- Divide \( x^3 \) by \( x^2 \), which gives **\( x \)**.

### Step 2: Multiply
- Multiply \( x \) by \( (x^2 - 1) \), giving \( x^3 - x \).

### Step 3: Subtract
\[
(x^3 + 7x^2 - x - 7) - (x^3 - x) = 7x^2 - 7
\]

### Step 4: Divide again
- Divide \( 7x^2 \) by \( x^2 \), which gives **\( +7 \)**.

### Step 5: Multiply
- Multiply \( 7 \) by \( (x^2 - 1) \), giving \( 7x^2 - 7 \).

### Step 6: Subtract
\[
(7x^2 - 7) - (7x^2 - 7) = 0
\]

Since the remainder is **0**, the quotient is:

\[
x + 7
\]

So,

\[
(x^3 + 7x^2 - x - 7) \div (x^2 - 1) = x + 7
\]

Yusmud

1 year ago

No explanation 😓