On dividing `p ( 4p ^(2) - 16)` by `4p (p-2),` we get

Options

A. `2p + 4`
B. `2p -4`
C. `p+2`
D. `p -2`

Answer

To solve the problem of dividing \( p(4p^2 - 16) \) by \( 4p(p - 2) \), we can follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \frac{p(4p^2 - 16)}{4p(p - 2)} \]

### Step 2: Factor the numerator
Notice that \( 4p^2 - 16 \) can be factored. It is a difference of squares:
\[ 4p^2 - 16 = 4(p^2 - 4) = 4(p - 2)(p + 2) \]
So we can rewrite the numerator:
\[ p(4p^2 - 16) = p \cdot 4(p - 2)(p + 2) = 4p(p - 2)(p + 2) \]

### Step 3: Substitute back into the expression
Now we substitute this back into our original expression:
\[ \frac{4p(p - 2)(p + 2)}{4p(p - 2)} \]

### Step 4: Cancel common terms
We can cancel \( 4p \) and \( (p - 2) \) from the numerator and the denominator:
\[ \frac{4p(p - 2)(p + 2)}{4p(p - 2)} = p + 2 \]

### Step 5: Conclusion
Thus, the result of dividing \( p(4p^2 - 16) \) by \( 4p(p - 2) \) is:
\[ p + 2 \]

### Final Answer
The final answer is \( p + 2 \).

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