# Factor completely x² - 10x + 25.

(x - 5)(x - 5), (x + 5)(x + 5), (x + 5)(x - 5), (x - 25)(x - 1)

**Solution:**

Given is a quadratic polynomial.

**Step 1: **Identify the values of a, b and c.

In the above equation, a is coefficient of x^{2} = 1,

b is the coefficient of x = -10 and

c is the constant term = 25.

**Step 2: **Solve for x by factoring polynomial by splitting the middle term.

Multiply a and c and find the factors that add up to b.

1 × (25) = 25

⇒ -5 and -5 add up to b. -5 is a factor of 25.

**Step 3: **Split bx into two terms.

x² - 5x - 5x + 25

**Step 4: **Take out the common factors by grouping.

x(x - 5) - 5(x - 5)

(x - 5) (x - 5) or (x - 5)^{2}

Thus the factors of the given polynomial x² - 10x + 25 are (x - 5) (x - 5)

## Factor completely x² - 10x + 25.

(x - 5)(x - 5), (x + 5)(x + 5), (x + 5)(x - 5), (x - 25)(x - 1)

**Summary:**

The factors of the equation x² - 10x + 25 are (x - 5) (x - 5).