The modified expression, $x^3(2 x+5)-4(2 x+5)$, has two terms with a common factor:
The given expression is \(x^3(2x+5) - 4(2x+5)\). This expression consists of two terms:
To find the common factor, we look for an expression that multiplies both terms. By inspecting both parts of the expression, we can clearly see that \((2x+5)\) appears as a multiplier in both terms. Therefore, \((2x+5)\) is the common factor of the entire expression.
Now we compare the identified common factor, \((2x+5)\), with the given options:
Option c matches our identified common factor \((2x+5)\). Thus, the correct choice is c.
In many areas of algebra, such as simplifying expressions or solving equations, finding a common factor is a foundational skill. For example, in physics, when calculating total work done by forces on an object, you might find an expression like \(F_1d + F_2d\). Here, the displacement \(d\) is the common factor, and identifying it allows you to rewrite the expression as \(d(F_1 + F_2)\), which simplifies your calculations and gives you a clearer physical understanding of the work being done. Mastery of factoring helps in making complex systems more manageable and intuitive.