Factor x^2-5x+6
Factor polynomials completely: trinomials, difference of squares, sum/difference of cubes.
To factor the trinomial x^2-5x+6, find two numbers that multiply to the constant term and add to the coefficient of x.
x2-5x+6
Identify the coefficients: a = 1, b = -5, c = 6
For a trinomial x2 + bx + c, we need two numbers p and q where:
p × q = 6 (the constant term)
p + q = -5 (the coefficient of x)
This works because (x + p)(x + q) = x2 + (p+q)x + pq.
-3 × -2 = 6, -3 + (-2) = -5 → use -3 and -2
Rewrite −5x as −3x and −2x:
x2 − 3x − 2x + 6
(x2 - 3x) + (6 - 2x)
Factor the GCF from each group:
(x2 - 3x) = x(x - 3)
(6 - 2x) = -2(x - 3)
Both groups share the same binomial factor — pull it out:
= (x - 3)(x - 2)
(x - 3)(x - 2)
How to factor x^2-5x+6
To factor x^2-5x+6, identify the type of polynomial and apply the appropriate technique. The factored form is (x - 3)(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 x^2-5x+6?
The answer is (x - 3)(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.