Answer:
polynomial is one. Because the zeros of a polynomial can be determined from the factors of a polynomial, the factors can be created from the zeros. For the zero which occurs at 2, 3 x x = -2/3, the factor which produced that zero is 2. 3 x §· ¨¸ ©¹ The multiplicity represents how many times that zero occurs, in other words, the degree of ...
Step-by-step explanation:
The answer to this rests on knowing that there are four properties of multiplication (which your teacher will likely expect you to know...):
These are:
1. commutative
2. associative
3. multiplicative identity
4. distributive
I won't define each of these -- they should be in your notes or textbook. Look them up.
In this case, we are multiplying three terms together -- on the left hand side the parentheses mean to multiply a and b first, then multiply that by 3. On the right hand side, we multiply b times 3 first, and then multiply the product by a.
This would be an example of the associative property of multiplication: when three or more factors are multiplied together, the product is the same regardless of how the factors are grouped.
Hope this helps!
Good luck
![\left[ \begin{matrix} 2 & a \\ -1 & -2 \end{matrix} \right] + \left[ \begin{matrix} b & 4 \\ -2 & 1 \end{matrix} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Bmatrix%7D%202%20%26%20a%20%5C%5C%20-1%20%26%20-2%20%5Cend%7Bmatrix%7D%20%5Cright%5D%20%2B%20%5Cleft%5B%20%5Cbegin%7Bmatrix%7D%20b%20%26%204%20%5C%5C%20-2%20%26%201%20%5Cend%7Bmatrix%7D%20%5Cright%5D)
This addition of matrices can be combined into one matrix.
To add matrices, add the corresponding components of each matrix.
After adding, we'll have the following
![\left[ \begin{matrix} 2+b & a+4 \\ -3 & -1 \end{matrix} \right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%20%5Cbegin%7Bmatrix%7D%202%2Bb%20%26%20a%2B4%20%5C%5C%20-3%20%26%20-1%20%5Cend%7Bmatrix%7D%20%5Cright%5D%20)
This matrix should be equal to the matrix on the right-hand side of the equation. This means that each corresponding component of this matrix and the other matrix should be equivalent.
This means that
AND
Solving these one-step equations will give the values of a = -4 and b = -1. That's answer choice D.
