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) + (2x + 6)
Factor the GCF from each group:
(x2 + 3x) = x(x + 3)
(2x + 6) = 2(x + 3)
Both groups share the same binomial factor — pull it out:
= (x + 2)(x + 3)
(x + 2)(x + 3)
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 + 2)(x + 3).
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 + 2)(x + 3).
What method is used?
identifying the polynomial type and applying the matching technique — GCF, trinomial factoring, difference of squares, or special cube formulas.