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

5x−2
5 x minus 2

12x−2
12 x minus 2

12x+12
12 x plus 12

5x+12

Answer 1

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

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

We are given the area as \( 15x^2 + 14x - 8 \) and the length as \( 3x + 4 \). We can set up the equation:

\[
15x^2 + 14x - 8 = (3x + 4) \times \text{Width}
\]

To find the width, we can divide the area by the length:

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

Now, let's perform the polynomial long division:

1. Divide the first term of the numerator \( 15x^2 \) by the first term of the denominator \( 3x \), which gives us \( 5x \).
2. Multiply \( 5x \) by \( 3x + 4 \):

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

3. Subtract this result from the original polynomial:

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

4. Now, divide the first term of the new result \( -6x \) by the first term of the denominator \( 3x \), which gives us \( -2 \).
5. Multiply \( -2 \) by \( 3x + 4 \):

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

6. Subtract this from the previous result:

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

Therefore, the width is:

\[
\text{Width} = 5x - 2
\]

The correct answer is **5x - 2**.