Sure! To factor the given quadratic equation [tex]\(x^2 - 4x + 4 = 0\)[/tex] into two linear factors, we'll follow these steps:
1. Identify the coefficients: In the quadratic equation of the form [tex]\(ax^2 + bx + c = 0\)[/tex], the coefficients are:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = -4\)[/tex]
- [tex]\(c = 4\)[/tex]
2. Factoring the quadratic equation:
- First, we need to find two numbers that when multiplied give us [tex]\(a \cdot c = 1 \cdot 4 = 4\)[/tex] and when added give us [tex]\(b = -4\)[/tex].
- These two numbers are [tex]\(-2\)[/tex] and [tex]\(-2\)[/tex] because [tex]\((-2) \cdot (-2) = 4\)[/tex] and [tex]\((-2) + (-2) = -4\)[/tex].
3. Writing the equation in factored form:
- Using the numbers [tex]\(-2\)[/tex] and [tex]\(-2\)[/tex], the quadratic equation can be written as the product of two binomials:
[tex]\[
(x - 2)(x - 2) = 0
\][/tex]
- This can also be written in a more compact form as:
[tex]\[
(x - 2)^2 = 0
\][/tex]
So, the factored form of the quadratic equation [tex]\(x^2 - 4x + 4 = 0\)[/tex] is [tex]\((x - 2)^2 = 0\)[/tex].
Thus, the answer is:
[tex]\[
(x - 2)^2
\][/tex]
