Factor completely x² - 8x + 16
(x + 4)(x + 4), (x - 4)(x - 4), (x + 4)(x - 4), (x - 2)(x - 8)

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 = -8 and

c is the constant term = 16.

Step 2: Let us factorize the polynomial to find the value of x by splitting the middle term.

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

1 × (16) = 16

⇒ -4 and -4 add up to b. -4 is the factor of 16.

Step 3: Split bx into two terms.

x² - 4x - 4x + 16

Step 4: Take out the common factors by grouping.

x(x - 4) - 4(x - 4)

(x - 4) (x - 4) or (x - 4)²

Thus x² - 8x + 16 is factorized as (x + 4) (x+4)

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Factor completely x² - 8x + 16
(x + 4)(x + 4), (x - 4)(x - 4), (x + 4)(x - 4), (x - 2)(x - 8)

Summary:

The factors of the equation x² - 8x + 16 are (x - 4) (x - 4).