Question

the area of a rectangle of width ( w ) is given by ( a = 5w^2 + w ).
factor the right - hand side of the equation to find an expression for the length of the rectangle.
( l=square )

Explanation:

Step1: Identify the GCF

The terms \(5w^2\) and \(w\) have a greatest common factor (GCF) of \(w\).

Step2: Factor out the GCF

Factor out \(w\) from \(5w^2 + w\):
\(5w^2 + w = w(5w + 1)\)
Since the area of a rectangle is \(A = l \times w\), and \(A = w(5w + 1)\), the length \(l\) is \(5w + 1\).

Answer:

\(5w + 1\)