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 x² = 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)

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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).