The given expression is 4w - 10, which represents the area of a rectangle. To factor this expression, we need to find two numbers whose product is equal to 4w - 10 and whose sum is equal to the coefficient of the linear term, which is 4w.
Let's consider the expression 4w - 10. To factor it, we need to find two numbers that multiply to give us -10 and add up to give us 4. In this case, the numbers are 5 and -2 because 5 * (-2) = -10 and 5 + (-2) = 4.
So, we can factor the expression 4w - 10 as (4w + 5)(w - 2).
Now, let's interpret what this factored expression tells us about the dimensions of the rectangle.
The factored expression (4w + 5)(w - 2) indicates that the rectangle has two dimensions: 4w + 5 and w - 2.
The dimension 4w + 5 represents the length of the rectangle, while the dimension w - 2 represents the width of the rectangle.
This means that the length of the rectangle is 4w + 5 units, and the width of the rectangle is w - 2 units.
Therefore, we can conclude that the dimensions of the rectangle are given by (4w + 5) units for the length and (w - 2) units for the width.