`(3)/(5)x^2-(19)/(5)x+4`

Answer

To factor the polynomial \(\frac{3}{5}x^2 - \frac{19}{5}x + 4\), we will follow these steps:

### Step 1: Rewrite the expression
Start with the given expression:
\[ \frac{3}{5}x^2 - \frac{19}{5}x + 4 \]

### Step 2: Eliminate the fraction
To make calculations easier, we can multiply the entire expression by 5 (the denominator) to eliminate the fractions:
\[ 5 \left(\frac{3}{5}x^2 - \frac{19}{5}x + 4\right) = 3x^2 - 19x + 20 \]

### Step 3: Factor the quadratic expression
Now we need to factor the quadratic \(3x^2 - 19x + 20\). We will look for two numbers that multiply to \(3 \times 20 = 60\) and add up to \(-19\). The numbers that satisfy this are \(-15\) and \(-4\).

### Step 4: Rewrite the middle term
We can rewrite the expression by splitting the middle term using the numbers found:
\[ 3x^2 - 15x - 4x + 20 \]

### Step 5: Group the terms
Now, group the terms:
\[ (3x^2 - 15x) + (-4x + 20) \]

### Step 6: Factor by grouping
Factor out the common factors from each group:
\[ 3x(x - 5) - 4(x - 5) \]

### Step 7: Factor out the common binomial
Now, we can factor out the common binomial \((x - 5)\):
\[ (3x - 4)(x - 5) \]

### Step 8: Write the final expression
Now, we can write the expression in its factored form:
\[ \frac{1}{5} (3x - 4)(x - 5) \]

### Final Answer
Thus, the factored form of the polynomial \(\frac{3}{5}x^2 - \frac{19}{5}x + 4\) is:
\[ \frac{1}{5} (3x - 4)(x - 5) \]