Question

the area of a rectangle is found by multiplying the base times the height. a rectangle with an area represented by $12x^{2}+6x - 8$ has a height of $4x$. what is the base of the rectangle? $3x+\frac{3}{2}-\frac{2}{x}$ $3x^{2}+\frac{3}{2}-\frac{2}{x}$ $3x+\frac{3x}{2}-\frac{2}{x}$ $3x+\frac{3}{2}-\frac{1}{2x}$

Explanation:

Step1: Recall the formula for the area of a rectangle

The area formula of a rectangle is \(A = b\times h\), where \(A\) is the area, \(b\) is the base, and \(h\) is the height. We need to find \(b\), so \(b=\frac{A}{h}\). Given \(A = 12x^{2}+6x - 8\) and \(h = 4x\).

Step2: Divide each term of the polynomial by \(4x\)

• Divide \(12x^{2}\) by \(4x\): \(\frac{12x^{2}}{4x}=3x\).
• Divide \(6x\) by \(4x\): \(\frac{6x}{4x}=\frac{3}{2}\).
• Divide \(- 8\) by \(4x\): \(\frac{-8}{4x}=-\frac{2}{x}\).

Answer:

\(3x+\frac{3}{2}-\frac{2}{x}\) (the first option)