the sum of two polynomials is -yz² - 3z² - 4y + 4. if one of the polynomials is y - 4yz² - 3, what is the…

Explanation:

Step1: Let the unknown polynomial be $P$.

Let the sum of the two polynomials be $S=-yz^{2}-3z^{2}-4y + 4$ and one polynomial be $A=y - 4yz^{2}-3$. We know that $S=A + P$, so $P=S - A$.

Step2: Substitute the polynomials into the formula.

$P=(-yz^{2}-3z^{2}-4y + 4)-(y - 4yz^{2}-3)$

Step3: Remove the parentheses.

$P=-yz^{2}-3z^{2}-4y + 4 - y+4yz^{2}+3$

Step4: Combine like - terms.

For the $yz^{2}$ terms: $-yz^{2}+4yz^{2}=3yz^{2}$; for the $y$ terms: $-4y - y=-5y$; for the constant terms: $4 + 3 = 7$; and the $z^{2}$ term remains $-3z^{2}$. So $P=3yz^{2}-3z^{2}-5y + 7$.

Answer:

D. $3yz^{2}-3z^{2}-5y + 7$