Factor 2x^3-x^2-5x-2
Factor polynomials completely: trinomials, difference of squares, sum/difference of cubes.
To factor 2x^3-x^2-5x-2, look for patterns like grouping, difference of squares, or rational roots.
2x3-x2-5x-2
By the Rational Root Theorem, any rational root p/q must have p dividing the constant term and q dividing the leading coefficient:
Factors of constant (2): ±{1, 2}
Factors of leading (2): ±{1, 2}
Candidates: 12, -12, 1, -1, 2, -2
Substitute x = -1/2 into the polynomial:
f(-12) = 2(-12)3 − (-12)2 − 5(-12) − 2 = 0
f(-12) = 0 ✓ → (x + 12) is a factor
Perform synthetic division by (x + 1/2):
[2 | -1 | -5 | -2] ÷ (-12) → [2 | -2 | -4]
Quotient: 2x2 − 2x − 4
Factor 2x^2 − 2x − 4:
= 2(x - 2)(x + 1)
= (x - 2)(x + 1)(2x + 1)
(x - 2)(x + 1)(2x + 1)
How to factor 2x^3-x^2-5x-2
To factor 2x^3-x^2-5x-2, identify the type of polynomial and apply the appropriate technique. The factored form is (x - 2)(x + 1)(2x + 1).
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 2x^3-x^2-5x-2?
The answer is (x - 2)(x + 1)(2x + 1).
What method is used?
identifying the polynomial type and applying the matching technique — GCF, trinomial factoring, difference of squares, or special cube formulas.