`h(x)=-2(x^(2)-5x+3)+7(c-x)`
In the polynomial `h(x)` defined above, c is a constant. If `h(x)` is divisible by x, what is the value of c?

Options

A. `-(6)/(7)`
B. 0
C. `(6)/(7)`
D. 6

Answer

To solve the problem, we start with the polynomial given:

\[ h(x) = -2(x^2 - 5x + 3) + 7(c - x) \]

### Step 1: Expand the polynomial
First, we will expand the polynomial by distributing the constants:

\[ h(x) = -2(x^2) + 10x - 6 + 7c - 7x \]

### Step 2: Combine like terms
Next, we combine the like terms in the polynomial:

\[ h(x) = -2x^2 + (10x - 7x) + (7c - 6) \]

This simplifies to:

\[ h(x) = -2x^2 + 3x + (7c - 6) \]

### Step 3: Set the constant term to zero
For \( h(x) \) to be divisible by \( x \), the constant term must equal zero. The constant term in our polynomial is \( 7c - 6 \). Therefore, we set it to zero:

\[ 7c - 6 = 0 \]

### Step 4: Solve for \( c \)
Now, we solve for \( c \):

\[ 7c = 6 \]
\[ c = \frac{6}{7} \]

### Conclusion
Thus, the value of \( c \) is:

\[ \boxed{\frac{6}{7}} \]