Factor x^2-4x+4
Factor polynomials completely: trinomials, difference of squares, sum/difference of cubes.
To factor the trinomial x^2-4x+4, find two numbers that multiply to the constant term and add to the coefficient of x.
x2-4x+4
Identify the coefficients: a = 1, b = -4, c = 4
Check if this is a perfect square trinomial by verifying three conditions:
1. Is the first term a perfect square? (x)2 = x2 ✓
2. Is the last term a perfect square? 22 = 4 ✓
3. Is the middle term = 2(x)(2) = 4x? ✓
All three conditions are satisfied — this is a perfect square trinomial.
Apply the formula: (a − b)² = a² − 2ab + b²
= (x − 2)2
(x - 2)2
How to factor x^2-4x+4
To factor x^2-4x+4, identify the type of polynomial and apply the appropriate technique. The factored form is (x - 2)^2.
This is a polynomial factoring problem — we break a polynomial into a product of simpler expressions. Common methods include GCF extraction, difference of squares, and trinomial factoring.
Frequently asked questions
What is the answer to x^2-4x+4?
The answer is (x - 2)^2.
What method is used?
identifying the polynomial type and applying the matching technique — GCF, trinomial factoring, difference of squares, or special cube formulas.