Question

6.03 dividing polynomials by a monomial

1. the rectangle shown below has an area of $3x^4 - 6x$ square units.

find a polynomial expression for its length.
length =

Explanation:

Step1: Recall area formula for rectangle

Area = length $\times$ width

Step2: Isolate length variable

$\text{length} = \frac{\text{Area}}{\text{width}}$

Step3: Substitute given values

$\text{length} = \frac{3x^4 - 6x}{3x}$

Step4: Split the fraction

$\text{length} = \frac{3x^4}{3x} - \frac{6x}{3x}$

Step5: Simplify each term

$\text{length} = x^3 - 2$

Answer:

$\boldsymbol{x^3 - 2}$