Factor 3x^2-12
Factor polynomials completely: trinomials, difference of squares, sum/difference of cubes.
To factor 3x^2-12, recognize this as a difference of two squares — a² − b² = (a + b)(a − b).
3x2-12
-12 ÷ 3 = -4
3x2 ÷ 3 = x2
= 3(x2 − 4)
This expression has two terms connected by subtraction, and both are perfect squares. This matches the difference of squares pattern.
The identity states:
a2 − b2 = (a + b)(a − b)
Identify a and b:
a = x (since (x)2 gives the first term)
b = 2 (since 22 = 4)
Substitute a and b into (a + b)(a − b):
= (x + 2)(x − 2)
3(x - 2)(x + 2)
How to factor 3x^2-12
To factor 3x^2-12, identify the type of polynomial and apply the appropriate technique. The factored form is 3(x - 2)(x + 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 3x^2-12?
The answer is 3(x - 2)(x + 2).
What method is used?
identifying the polynomial type and applying the matching technique — GCF, trinomial factoring, difference of squares, or special cube formulas.