Factor x^2+2x-15

Factor polynomials completely: trinomials, difference of squares, sum/difference of cubes.

Expression

Answer

(x - 3)(x + 5)

To factor the trinomial x^2+2x-15, find two numbers that multiply to the constant term and add to the coefficient of x.

x²+2x-15

Step 1 — Factor x² + 2x − 15

Identify the coefficients: a = 1, b = 2, c = -15

Step 2 — Find the factor pair

For a trinomial x² + bx + c, we need two numbers p and q where:

p × q = -15 (the constant term)

p + q = 2 (the coefficient of x)

This works because (x + p)(x + q) = x² + (p+q)x + pq.

5 × -3 = -15, 5 + (-3) = 2 → use 5 and -3

Step 3 — Split the middle term

Rewrite +2x as +5x and −3x:

x² + 5x − 3x − 15

Step 4 — Factor by grouping

(x² + 5x) + (-3x - 15)

Factor the GCF from each group:

(x² + 5x) = x(x + 5)

(-3x - 15) = -3(x + 5)

Both groups share the same binomial factor — pull it out:

= (x - 3)(x + 5)

(x - 3)(x + 5)

How to factor x^2+2x-15

To factor x^2+2x-15, identify the type of polynomial and apply the appropriate technique. The factored form is (x - 3)(x + 5).

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+2x-15?
The answer is (x - 3)(x + 5).

What method is used?
identifying the polynomial type and applying the matching technique — GCF, trinomial factoring, difference of squares, or special cube formulas.