To find the missing polynomial [tex]\( ? \)[/tex], we start with the given equation:
[tex]\[ ? - (20 - 4x - 5x^2) = 20 - 7x^2 \][/tex]
First, we rearrange the equation to isolate the missing polynomial [tex]\( ? \)[/tex]:
[tex]\[ ? = (20 - 7x^2) + (20 - 4x - 5x^2) \][/tex]
Next, we combine like terms on the right-hand side of the equation:
- The constant terms: [tex]\( 20 + 20 = 40 \)[/tex]
- The linear terms: [tex]\( -4x \)[/tex]
- The quadratic terms: [tex]\( -7x^2 + -5x^2 = -12x^2 \)[/tex]
So, the polynomial [tex]\( ? \)[/tex] is:
[tex]\[ ? = 40 - 4x - 12x^2 \][/tex]
Therefore, the missing polynomial is:
[tex]\[ 40 - 4x - 12x^2 \][/tex]
Thus, the correct choice from the given options is:
[tex]\[ \boxed{40 - 4x - 12x^2} \][/tex]
