actor completely. $$ 3 x^{2}-20 x+25 $$

Question

UpStudy AI · Accepted Answer

It looks like you want to **factor completely** the quadratic expression:

$$
3x^{2} - 20x + 25
$$

Let's factor this step by step.

### Step 1: Identify the Coefficients
The quadratic is in the form:
$$
ax^{2} + bx + c
$$
Where:
- $$ a = 3 $$
- $$ b = -20 $$
- $$ c = 25 $$

### Step 2: Multiply $$ a $$ and $$ c $$
Multiply the coefficients of $$ x^{2} $$ and the constant term:
$$
a \times c = 3 \times 25 = 75
$$

### Step 3: Find Two Numbers That Multiply to $$ a \times c $$ and Add to $$ b $$
We need two numbers that:
- Multiply to **75**
- Add up to **-20**

The numbers are **-5** and **-15** because:
$$
-5 \times -15 = 75 \
-5 + (-15) = -20
$$

### Step 4: Rewrite the Middle Term Using These Numbers
Rewrite the quadratic expression by splitting the middle term:
$$
3x^{2} - 5x - 15x + 25
$$

### Step 5: Factor by Grouping
Group the terms into two pairs:
$$
(3x^{2} - 5x) - (15x - 25)
$$

Factor out the greatest common factor (GCF) from each group:
$$
x(3x - 5) - 5(3x - 5)
$$

### Step 6: Factor Out the Common Binomial Factor
Both groups contain the common factor $$ (3x - 5) $$:
$$
(3x - 5)(x - 5)
$$

### Final Factored Form
$$
3x^{2} - 20x + 25 = (3x - 5)(x - 5)
$$

**Therefore, the completely factored form of the quadratic expression is:**

$$
(3x - 5)(x - 5)
$$
The quadratic expression $$ 3x^{2} - 20x + 25 $$ factors completely to $$ (3x - 5)(x - 5) $$.

actor completely. \[ 3 x^{2}-20 x+25 \]