Respuesta :
Let's call the two polynomials [tex] p_1, p_2 [/tex]. Assume, for example, that [tex] p_1[/tex] is the known one. So, we have two pieces of information:
[tex] \begin{cases} p_1 = y - 4yz^2 - 3 \\ p_1+p_2 = -yz^2 - 3z^2 - 4y + 4 \end{cases} [/tex]
If you subtract the first equation from the second, you get
[tex] (p_1+p_2)-p_1 = -yz^2 - 3z^2 - 4y + 4 - (y - 4yz^2 - 3) [/tex]
The left hand side evaluates to [tex]p_2 [/tex], so the right hand side is its expression:
[tex] p_2 = -yz^2 - 3z^2 - 4y + 4 - y + 4yz^2 + 3 [/tex]
And if you sum like terms you get
[tex] p_2 = 3 y z^2 - 5 y - 3 z^2 + 7 [/tex]
Since sum of two polynomials is given and one of the polynomial is given, thus, you can subtract that given polynomial from the sum to get the other polynomial which was used with given polynomial to find the sum.
The other polynomial is [tex]3yz^2 - 3z^2 -5y + 7[/tex]
How to find the difference of polynomials?
For given two polynomials, to find the difference, we first it as a simple subtraction. Then we get that negative sign in middle to affect sign of the later polynomial.
Positive sign will become negative since negative times positive is negative and the negative signs will become positive as negative times negative is positive. Then we collect all the like terms (those terms which have same variables with same power).
How to find the other polynomial in the given context?
Let the sum of the polynomials be denoted by S(y,z).
Then we have:
[tex]S(y,z) = -yz^2 -3z^2 - 4y +4[/tex]
Let first polynomial be denoted by [tex]P_1(y,z)[/tex]. Then we have:
[tex]P_1(y,z) = y - 4yz^2 - 3[/tex]
Let the second polynomial is denoted by [tex]P_2(y,z)[/tex]. Thus, we have:
[tex]P_1(y, z) + P_2(y,z) = S(y,z)\\P_2(y,z) = S(y,z) - P_1(y,z)\\P_2(y,z) = (-yz^2 - 3z^2 - 4y + 4) - (y - 4yz^2 -3)\\ \\P_2(y,z) = -yz^2 - 3z^2 - 4y + 4 - y + 4yz^2 + 3\\P_2(y,z) = (-yz^2 + 4yz^2) - 3z^2 + (-4y - y) + (4+3)\\P_2(y,z) = ( 4yz^2 - 1 \times yz^2) - 3z^2 + (-4y - 1 \times y) + 7\\P_2(y,z) = 3yz^2 - 3z^2 -5y + 7[/tex]
Note how sign changes as we open brackets. When negative sign is outside the bracket, all sign will flip(negative becomes positive and positive will become negative)
If positive is outside, all sign remain same.
Thus, the other polynomial is [tex]3yz^2 - 3z^2 -5y + 7[/tex]
Learn more about subtraction of polynomials here:
https://brainly.com/question/9351663
