Question

Find the quotient when (21x^2 - 52x +32) is divided by (7x-8)

Answer 1

To divide the polynomial \( 21x^2 - 52x + 32 \) by \( 7x - 8 \), we can use polynomial long division.

1. **Divide the leading terms**:
\[ \frac{21x^2}{7x} = 3x \]

2. **Multiply** \( 3x \) by \( 7x - 8 \):
\[ 3x(7x - 8) = 21x^2 - 24x \]

3. **Subtract** this from the original polynomial:
\[
(21x^2 - 52x + 32) - (21x^2 - 24x) = -52x + 24x + 32 = -28x + 32
\]

4. **Repeat the process** with the new polynomial \( -28x + 32 \):
- Divide the leading term:
\[ \frac{-28x}{7x} = -4 \]

5. **Multiply** \( -4 \) by \( 7x - 8 \):
\[ -4(7x - 8) = -28x + 32 \]

6. **Subtract**:
\[
(-28x + 32) - (-28x + 32) = 0
\]

Since we've reached a remainder of 0, the division is complete.

The quotient when \( 21x^2 - 52x + 32 \) is divided by \( 7x - 8 \) is:
\[
\boxed{3x - 4}
\]