Question

what is the missing polynomial?

\\(?\\) \\(- (20 - 4x - 5x^2) = 20 - 7x^2\\)

• \\(4x - 12x^2\\)
• \\(4x - 2x^2\\)
• \\(40 - 4x - 12x^2\\)
• \\(40 - 4x - 2x^2\\)

Explanation:

⚡ Using what you learned: adding and subtracting polynomials

Step 1: Set up the equation

Let \( P \) represent the missing polynomial:

$$ P - (20 - 4x - 5x^2) = 20 - 7x^2 $$

Step 2: Isolate the missing polynomial

Add \( (20 - 4x - 5x^2) \) to both sides of the equation:

$$ P = (20 - 7x^2) + (20 - 4x - 5x^2) $$

Step 3: Combine like terms

Group the constant terms, the \( x \) terms, and the \( x^2 \) terms:

$$ P = (20 + 20) - 4x + (-7x^2 - 5x^2) $$

$$ P = 40 - 4x - 12x^2 $$

Answer:

\( 40 - 4x - 12x^2 \)