Solve the equation by the zero-factor property. $$ c^{2}-10 c+16=0 $$

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To solve the quadratic equation $$ c^{2} - 10c + 16 = 0 $$ using the **zero-factor property**, follow these steps:

### Step 1: Factor the Quadratic Equation

We need to express the quadratic equation in its factored form. The goal is to find two numbers that multiply to **16** (the constant term) and add up to **-10** (the coefficient of the middle term).

Let's identify these two numbers:

- **Product:** $$ a \times b = 16 $$
- **Sum:** $$ a + b = -10 $$

Considering the signs, both numbers must be negative because their product is positive and their sum is negative.

Looking at the factors of 16:
- $$-2$$ and $$-8$$ satisfy both conditions:
  - $$ -2 \times -8 = 16 $$
  - $$ -2 + (-8) = -10 $$

So, the factored form of the quadratic equation is:
$$
c^{2} - 10c + 16 = (c - 2)(c - 8) = 0
$$

### Step 2: Apply the Zero-Product Property

According to the zero-product property, if the product of two factors is zero, at least one of the factors must be zero. Therefore, set each factor equal to zero:

1. $$ c - 2 = 0 $$
2. $$ c - 8 = 0 $$

### Step 3: Solve for $$ c $$

Solve each equation separately:

1. $$ c - 2 = 0 $$  
   $$ c = 2 $$

2. $$ c - 8 = 0 $$  
   $$ c = 8 $$

### **Solution:**

The solutions to the equation $$ c^{2} - 10c + 16 = 0 $$ are:
$$
c = 2 \quad \text{and} \quad c = 8
$$
The solutions are $$ c = 2 $$ and $$ c = 8 $$.

Solve the equation by the zero-factor property. \( c^{2}-10 c+16=0 \)

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