Question

The area of a rectangle is 15x2+14x−8 . The length of the rectangle is 3x+4 .

What is the width of the rectangle?

(1 point)
Responses

12x−212 x minus 2

5x+125 x plus 12

5x−25 x minus 2

12x+12

Answer 1

To find the width of the rectangle, you can use the formula for the area of a rectangle, which is:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

Given that the area is \( 15x^2 + 14x - 8 \) and the length is \( 3x + 4 \), you can solve for the width (let's call it \( w \)) using the equation:

\[
15x^2 + 14x - 8 = (3x + 4) \times w
\]

To find \( w \), divide the area by the length:

\[
w = \frac{15x^2 + 14x - 8}{3x + 4}
\]

Now, perform polynomial long division or synthetic division.

1. **Divide \( 15x^2 \) by \( 3x \)** to get \( 5x \).
2. **Multiply \( (3x + 4) \) by \( 5x \)**:

\[
5x(3x + 4) = 15x^2 + 20x
\]

3. **Subtract this from the original polynomial**:

\[
(15x^2 + 14x - 8) - (15x^2 + 20x) = 14x - 20x - 8 = -6x - 8
\]

4. Now, divide \(-6x\) by \(3x\) to get \(-2\).
5. **Multiply \( (3x + 4) \) by \(-2\)**:

\[
-2(3x + 4) = -6x - 8
\]

6. **Subtract this from the current remainder**:

\[
(-6x - 8) - (-6x - 8) = 0
\]

Thus, the width \( w = 5x - 2 \).

So, the width of the rectangle is **\( 5x - 2 \)**.