Coefficient of x in (` x+ 9) (8-5x)` is

Options

A. 37
B. `-53`
C. `-37`
D. 53

Answer

To find the coefficient of \( x \) in the expression \( (x + 9)(8 - 5x) \), we will follow these steps:

### Step 1: Expand the expression
We need to multiply the two binomials \( (x + 9) \) and \( (8 - 5x) \).

\[ (x + 9)(8 - 5x) = x \cdot 8 + x \cdot (-5x) + 9 \cdot 8 + 9 \cdot (-5x) \]

### Step 2: Calculate each term
Now we calculate each term:

1. \( x \cdot 8 = 8x \)
2. \( x \cdot (-5x) = -5x^2 \)
3. \( 9 \cdot 8 = 72 \)
4. \( 9 \cdot (-5x) = -45x \)

Putting it all together, we have:

\[ 8x - 5x^2 + 72 - 45x \]

### Step 3: Combine like terms
Now, we combine the like terms, particularly the \( x \) terms:

\[ 8x - 45x = -37x \]

So, the expression simplifies to:

\[ -5x^2 - 37x + 72 \]

### Step 4: Identify the coefficient of \( x \)
The coefficient of \( x \) in the expression \( -5x^2 - 37x + 72 \) is \( -37 \).

Thus, the coefficient of \( x \) is:

\[ \text{Coefficient of } x = -37 \]

### Final Answer
The coefficient of \( x \) is \( -37 \).

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