To combine and simplify the expression \((3x + 7)(2x - 5)\) and write it in standard form, we start by using the distributive property (also known as the FOIL method for binomials).
-
First: Multiply the first terms:
\[ 3x \cdot 2x = 6x^2 \] -
Outer: Multiply the outer terms:
\[ 3x \cdot (-5) = -15x \] -
Inner: Multiply the inner terms:
\[ 7 \cdot 2x = 14x \] -
Last: Multiply the last terms:
\[ 7 \cdot (-5) = -35 \]
Now, combine all these results together: \[ 6x^2 - 15x + 14x - 35 \]
Next, combine like terms: \[ -15x + 14x = -1x \text{ or } -x \]
So, the polynomial in descending order is: \[ 6x^2 - x - 35 \]
Thus, the final answer is: \[ \boxed{6x^2 - x - 35} \]