Answer:
To express the given expression in the form \(a \cdot x^3 + b \cdot x^2 + c \cdot x + d\), let's expand and simplify \((x + 1)(x + 3)(x + 5)\):
\((x + 1)(x + 3)(x + 5) = x^3 + (1+3+5)x^2 + (1 \cdot 3 + 1 \cdot 5 + 3 \cdot 5)x + (1 \cdot 3 \cdot 5)\)
Now, simplify the coefficients:
\(= x^3 + 9x^2 + 19x + 15\)
So, the expression can be written in the desired form as \(x^3 + 9x^2 + 19x + 15\), where \(a = 1\), \(b = 9\), \(c = 19\), and \(d = 15\), all of which are positive integers.
