One of the dimensions of the cuboid whose volume is `16x^(2)-26x+10` is

Options

A. `2`
B. `(8x-5)`
C. `(x-1)`
D. All of these

Answer

To find one of the dimensions of the cuboid whose volume is given by the polynomial \(16x^2 - 26x + 10\), we will factor the polynomial step by step.

### Step 1: Write down the volume expression
The volume of the cuboid is given as:
\[ V = 16x^2 - 26x + 10 \]

### Step 2: Factor out the common factor
First, we can factor out the greatest common factor from the polynomial. Here, we can factor out \(2\):
\[ V = 2(8x^2 - 13x + 5) \]

### Step 3: Factor the quadratic expression
Next, we need to factor the quadratic expression \(8x^2 - 13x + 5\). We will look for two numbers that multiply to \(8 \times 5 = 40\) and add up to \(-13\). The numbers \(-8\) and \(-5\) satisfy this condition because:
\[ -8 \times -5 = 40 \quad \text{and} \quad -8 + -5 = -13 \]

### Step 4: Rewrite the quadratic expression
Now we can rewrite the quadratic expression:
\[ 8x^2 - 8x - 5x + 5 \]

### Step 5: Group the terms
Next, we will group the terms:
\[ (8x^2 - 8x) + (-5x + 5) \]

### Step 6: Factor by grouping
Now, we can factor out the common factors from each group:
\[ 8x(x - 1) - 5(x - 1) \]

### Step 7: Factor out the common binomial
Now we can factor out the common binomial \((x - 1)\):
\[ (8x - 5)(x - 1) \]

### Step 8: Write the final factored form
Now, substituting back into the volume expression, we have:
\[ V = 2(8x - 5)(x - 1) \]

### Step 9: Identify the dimensions
From the factored form, we can identify the dimensions of the cuboid:
- One dimension is \(2\)
- Another dimension is \(8x - 5\)
- The third dimension is \(x - 1\)

### Conclusion
Thus, one of the dimensions of the cuboid is:
\[ \text{Dimension} = 2, \quad 8x - 5, \quad \text{or} \quad x - 1 \]