Question

determining a polynomial expression

the sum of two polynomials is (-yz^2 - 3z^2 - 4y + 4). if one of the polynomials is (y - 4yz^2 - 3), what is the other polynomial?

• (-2yz^2 - 4y + 7)
• (-2yz^2 - 3y + 1)
• (-5yz^2 + 3z^2 - 3y + 1)
• (3yz^2 - 3z^2 - 5y + 7)

Explanation:

Set up the subtraction equation

$$ P_{\text{other}} = (-yz^2 - 3z^2 - 4y + 4) - (y - 4yz^2 - 3) $$

Distribute the negative sign

$$ P_{\text{other}} = -yz^2 - 3z^2 - 4y + 4 - y + 4yz^2 + 3 $$

Combine like terms

$$
LATEXBLOCK0
$$

Answer:

• (A) \(-2yz^2 - 4y + 7\)
• (B) \(-2yz^2 - 3y + 1\)
• (C) \(-5yz^2 + 3z^2 - 3y + 1\)
• (D) \(3yz^2 - 3z^2 - 5y + 7\) (Correct answer)