The answer is the first one hope this helps!!
1 (B), because 3+-2=1, and 5+-4=1, which amounts to 1/1, or whole number 1.
Answer :
![6{y}^{4} {z}^{2} + 12 {y}^{3} {z}^{2}-3 {y}^{3} {z}+3 {y}^{2} {z}^{2}](https://tex.z-dn.net/?f=6%7By%7D%5E%7B4%7D%20%7Bz%7D%5E%7B2%7D%20%2B%2012%20%7By%7D%5E%7B3%7D%20%7Bz%7D%5E%7B2%7D-3%20%7By%7D%5E%7B3%7D%20%7Bz%7D%2B3%20%7By%7D%5E%7B2%7D%20%7Bz%7D%5E%7B2%7D)
Step-by-step explanation :
To find the product of
![3 {y}^{2} z(2 {y}^{2} z + 4yz - y + z)](https://tex.z-dn.net/?f=3%20%7By%7D%5E%7B2%7D%20z%282%20%7By%7D%5E%7B2%7D%20z%20%2B%204yz%20-%20y%20%2B%20z%29)
First we expand the bracket ,
it implies that, we use the expression outside the bracket to multiply individual expressions inside the bracket.
Hence
![3 {y}^{2} z(2 {y}^{2} z + 4yz - y + z)](https://tex.z-dn.net/?f=%203%20%7By%7D%5E%7B2%7D%20z%282%20%7By%7D%5E%7B2%7D%20z%20%2B%204yz%20-%20y%20%2B%20z%29)
![= 3 {y}^{2} z(2 {y}^{2} z) + 3 {y}^{2} z(4yz) - 3 {y}^{2} z(y )+3 {y}^{2} z( z)](https://tex.z-dn.net/?f=%20%3D%203%20%7By%7D%5E%7B2%7D%20z%282%20%7By%7D%5E%7B2%7D%20z%29%20%2B%203%20%7By%7D%5E%7B2%7D%20z%284yz%29%20-%203%20%7By%7D%5E%7B2%7D%20z%28y%20%29%2B3%20%7By%7D%5E%7B2%7D%20z%28%20z%29)
we now apply the law of indices
![{a}^{m} \times {a}^{n} = {a}^{m+n}](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7Bm%7D%20%5Ctimes%20%7Ba%7D%5E%7Bn%7D%20%3D%20%7Ba%7D%5E%7Bm%2Bn%7D)
meaning, when you are multiplying two expressions with the same bases , repeat one of the bases and add the exponents.
Then, simplify to obtain
ANSWER
The function that the given graph corresponds to is
![f(x) = (x - 2)(x - 1)(x + 1)(x + 2)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28x%20-%202%29%28x%20-%201%29%28x%20%2B%201%29%28x%20%20%2B%202%29)
EXPLANATION
The given graph in the attachment has x-intercepts at
![x = - 2 ,x=-1,x=1 \: \: and \: \: x=2](https://tex.z-dn.net/?f=x%20%3D%20%20-%202%20%2Cx%3D-1%2Cx%3D1%20%20%5C%3A%20%20%5C%3A%20and%20%20%20%5C%3A%20%5C%3A%20x%3D2)
These are the solutions of the polynomial function represented by the given graph.
We can write all these solutions as factors to obtain,
![x + 2 ,x + 1 ,x - 1 \: \:and \: \: x - 2](https://tex.z-dn.net/?f=x%20%20%2B%202%20%20%2Cx%20%2B%201%20%2Cx%20-%201%20%20%20%5C%3A%20%20%5C%3Aand%20%5C%3A%20%20%5C%3A%20x%20-%202%20)
The product of all these factors gives us the function whose graph was drawn.
This implies that,
![f(x) = (x - 2)(x - 1)(x + 1)(x + 2)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28x%20-%202%29%28x%20-%201%29%28x%20%2B%201%29%28x%20%20%2B%202%29)
Therefore the correct answer is option C.