Factor 6x^2+x-2
Factor polynomials completely: trinomials, difference of squares, sum/difference of cubes.
To factor 6x^2+x-2 with a leading coefficient of 6, use the AC method (factoring by grouping).
6x2+x-2
Identify the coefficients: a = 6, b = 1, c = -2
Since the leading coefficient is 6 (not 1), use the AC method:
Multiply the leading coefficient (a) by the constant term (c):
a × c = 6 × -2 = -12
Find two numbers that multiply to -12 and add to 1:
4 × -3 = -12, 4 + (-3) = 1 → use 4 and -3
Rewrite +x as +4x and −3x:
6x2 + 4x − 3x − 2
(6x2 + 4x) + (-3x - 2)
Factor the GCF from each group:
(6x2 + 4x) = 2x(3x + 2)
(-3x - 2) is already in the form 1 · (common factor)
Both groups share the same binomial factor — pull it out:
= (2x - 1)(3x + 2)
(2x - 1)(3x + 2)
How to factor 6x^2+x-2
To factor 6x^2+x-2, identify the type of polynomial and apply the appropriate technique. The factored form is (2x - 1)(3x + 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 6x^2+x-2?
The answer is (2x - 1)(3x + 2).
What method is used?
identifying the polynomial type and applying the matching technique — GCF, trinomial factoring, difference of squares, or special cube formulas.