Using the rule of addition in polynomial to solve the problem. Then the missing polynomial is [tex]-12x^{2} -4x+40[/tex].
It is an algebraic expression that consists of constant and variable. We can operate arithmetic operations such as addition, subtraction, multiplication, and division.
Like term
It means the like term can be added and subtracted only.
Rule for addition
In polynomial, the [tex]\rm x^{2}[/tex] term can be added with the only [tex]\rm x^{2}[/tex] term, the x term can be added with x only and the constant term can be added with the constant term only.
Let the missing polynomial be y.
[tex]\begin{aligned} y - (20 - 4x -5x^{2} ) &= 20 - 7x^{2} \\y &= 20 - 7x^{2} + (20 - 4x -5x^{2} )\\y &= -7x^{2} - 5x^{2} - 4x 20+20\\y &= -12x^{2} -4x +40\\\end{aligned}[/tex]
Thus, the missing polynomial is [tex]-12x^{2} -4x+40[/tex].
To more about the polynomial link is given below.
https://brainly.com/question/16059429
