The are of a rectangle is 4x²-13x-3, if its length is (x-3) find is width

The area of a rectangle is given by the formula:
\[
\text{Area} = \text{Length} \times \text{Width}.
\]

Given:
- Area = \( 4x^2 - 13x - 3 \)
- Length = \( x - 3 \)

To find the width, we can rearrange the area formula to solve for the width:
\[
\text{Width} = \frac{\text{Area}}{\text{Length}} = \frac{4x^2 - 13x - 3}{x - 3}.
\]

To divide \( 4x^2 - 13x - 3 \) by \( x - 3 \), we'll use polynomial division.

1. **Polynomial Division**:
   - Divide the first term of the numerator by the first term of the denominator:
     \[
     \frac{4x^2}{x} = 4x.
     \]
   - Multiply \( x - 3 \) by \( 4x \):
     \[
     4x \times (x - 3) = 4x^2 - 12x.
     \]
   - Subtract this product from the original polynomial:
     \[
     (4x^2 - 13x - 3) - (4x^2 - 12x) = -x - 3.
     \]
   - Now, divide the new first term by the first term of the denominator:
     \[
     \frac{-x}{x} = -1.
     \]
   - Multiply \( x - 3 \) by \( -1 \):
     \[
     -1 \times (x - 3) = -x + 3.
     \]
   - Subtract this from the previous result:
     \[
     (-x - 3) - (-x + 3) = -6.
     \]

The division shows that:
\[
4x^2 - 13x - 3 = (x - 3)(4x + 1).
\]

Therefore, the width of the rectangle is \( 4x + 1 \).

### Summary:
- **Width**: \( 4x + 1 \)

Would you like more details or have any questions?

### Related Questions:
1. How do you factor a quadratic expression?
2. What is the relationship between area, length, and width in a rectangle?
3. How do you use synthetic division for polynomial division?
4. Can all quadratic expressions be factored?
5. What happens if the divisor is not a factor of the polynomial?

**Tip:** When dividing polynomials, always double-check by multiplying the quotient by the divisor to ensure it equals the original polynomial.

The area of a rectangle is 4x² - 13x - 3. If its length is (x - 3), find its width.

Learn how to find the width of a rectangle when given the area 4x² - 13x - 3 and the length (x - 3). This solution covers polynomial division and factoring quadratics. Ideal for students in Grades 8-10.

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