Final answer:
The other polynomial is -2yz²-3y+1.
Step-by-step explanation:
To find the other polynomial, we need to subtract the given polynomial from the sum of the two polynomials.
Given polynomial: y-4yz²-3
Sum of the two polynomials: -yz²-3z²-4y+4
Subtracting the given polynomial from the sum, we get: (-yz²-3z²-4y+4) - (y-4yz²-3)
Simplifying, we get: -2yz²-3y+1
So, the other polynomial is -2yz²-3y+1. Therefore, the correct answer is option b.
Let's denote the other polynomial as
�
(
�
,
�
)
P(y,z). The sum of the two polynomials is given as:
�
−
4
�
�
2
−
3
+
�
(
�
,
�
)
=
−
�
�
2
−
3
�
2
−
4
�
+
4
y−4yz
2
−3+P(y,z)=−yz
2
−3z
2
−4y+4
To find
�
(
�
,
�
)
P(y,z), we can compare the coefficients of the corresponding terms on both sides of the equation.
Comparing the coefficients of
�
y:
1
+
�
�
=
−
4
1+P
y
=−4
�
�
=
−
5
P
y
=−5
Comparing the coefficients of
�
2
z
2
:
−
4
�
2
+
�
�
=
−
�
�
2
−
3
�
2
−4z
2
+P
z
=−yz
2
−3z
2
�
�
=
−
�
�
2
+
�
2
P
z
=−yz
2
+z
2
�
�
=
−
�
�
2
+
1
�
2
P
z
=−yz
2
+1z
2
Now, let's look at the answer choices:
a.
−
2
�
�
2
−
4
�
+
7
−2yz
2
−4y+7
b.
−
2
�
�
2
−
3
�
+
1
−2yz
2
−3y+1
c.
−
5
�
�
2
+
3
�
2
−
3
�
+
1
−5yz
2
+3z
2
−3y+1
d.
3
�
�
2
−
3
�
2
−
5
�
+
7
3yz
2
−3z
2
−5y+7
Among these, option (c)
−
5
�
�
2
+
3
�
2
−
3
�
+
1
−5yz
2
+3z
2
−3y+1 matches the values we obtained for
�
�
P
y
and
�
�
P
z
. Therefore, the other polynomial is
−
5
�
�
2
+
3
�
2
−
3
�
+
1
−5yz
2
+3z
2
−3y+1.