`28yz -21y^(3)z^(4) +35y^(2)z^(2) `= ______

Options

A. `7y^(2)x(4z-3yz^(3)+5z)`
B. `7yz(4-3y^(2)z^(3)+5yz)`
C. `7yz(4yz-3y^(2)z^(2)+5yz^(2))`
D. `7y^(2)z^(2)(4-3z^(2)+5)`

Answer

To factor the expression \( 28yz - 21y^3z^4 + 35y^2z^2 \), we will follow these steps:

### Step 1: Identify the common factors
We need to look for the greatest common factor (GCF) of the coefficients (28, -21, and 35) and the common variables in each term.

- The GCF of the coefficients:
- Factors of 28: \( 1, 2, 4, 7, 14, 28 \)
- Factors of 21: \( 1, 3, 7, 21 \)
- Factors of 35: \( 1, 5, 7, 35 \)

The GCF is 7.

- For the variable \( y \):
- The lowest power of \( y \) present in the terms is \( y^1 \).

- For the variable \( z \):
- The lowest power of \( z \) present in the terms is \( z^1 \).

Thus, the common factor we can take out is \( 7yz \).

### Step 2: Factor out the common factor
Now we will factor \( 7yz \) out of each term:

\[ 28yz = 7yz \cdot 4 \]
\[ -21y^3z^4 = 7yz \cdot (-3y^2z^3) \]
\[ 35y^2z^2 = 7yz \cdot 5y \]

### Step 3: Write the factored expression
Now we can write the expression as:

\[ 7yz(4 - 3y^2z^3 + 5y) \]

### Final Answer
The factored form of the expression \( 28yz - 21y^3z^4 + 35y^2z^2 \) is:

\[ 7yz(4 - 3y^2z^3 + 5y) \]

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