Use long division to divide. Specify the quotient and the remainder.
(4x2 − 9x − 9) ÷ (4x + 3)
quotient    	
 
remainder    	
  

We will perform long division to divide \( (4x^2 - 9x - 9) \) by \( (4x + 3) \).

### Step 1: Divide the first term of the dividend by the first term of the divisor.
- Dividend: \( 4x^2 - 9x - 9 \)
- Divisor: \( 4x + 3 \)

Divide \( 4x^2 \) (the first term of the dividend) by \( 4x \) (the first term of the divisor):

\[
\frac{4x^2}{4x} = x
\]

So, the first term of the quotient is \( x \).

### Step 2: Multiply the divisor by \( x \).
Now multiply the entire divisor \( 4x + 3 \) by \( x \):

\[
x(4x + 3) = 4x^2 + 3x
\]

### Step 3: Subtract this from the dividend.
Subtract \( 4x^2 + 3x \) from \( 4x^2 - 9x - 9 \):

\[
(4x^2 - 9x - 9) - (4x^2 + 3x) = -12x - 9
\]

### Step 4: Divide the new first term by the first term of the divisor.
Now, divide \( -12x \) by \( 4x \):

\[
\frac{-12x}{4x} = -3
\]

So, the second term of the quotient is \( -3 \).

### Step 5: Multiply the divisor by \( -3 \).
Multiply \( 4x + 3 \) by \( -3 \):

\[
-3(4x + 3) = -12x - 9
\]

### Step 6: Subtract this from the previous result.
Subtract \( -12x - 9 \) from \( -12x - 9 \):

\[
(-12x - 9) - (-12x - 9) = 0
\]

### Final Result:
The division has no remainder. So, the quotient is \( x - 3 \), and the remainder is 0.

### Answer:
- Quotient: \( x - 3 \)
- Remainder: 0

Would you like more details on any step? Here are some related questions:

1. How do you use synthetic division for polynomial division?
2. What is the difference between synthetic and long division for polynomials?
3. Can you explain the process of factoring quadratic polynomials?
4. How do you handle remainders in polynomial long division?
5. What are the steps to solve quadratic equations by completing the square?

**Tip:** Always align the terms based on their degrees during long division for clarity and accuracy!

Use long division to divide. Specify the quotient and the remainder.
(4x^2 − 9x − 9) ÷ (4x + 3)

Learn how to perform polynomial long division for the expression (4x^2 − 9x − 9) ÷ (4x + 3). This detailed guide walks through each step of the process, including calculating the quotient (x - 3) and determining there is no remainder. Suitable for students in Grades 9-11 studying algebra and polynomial division.

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