Factor x^3+x^2-4x-4
Factor polynomials completely: trinomials, difference of squares, sum/difference of cubes.
To factor x^3+x^2-4x-4, look for patterns like grouping, difference of squares, or rational roots.
x3+x2-4x-4
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 (4): ±{1, 2, 4}
Factors of leading (1): ±{1}
Candidates: 1, -1, 2, -2, 4, -4
Substitute x = -1 into the polynomial:
f(-1) = (-1)3 + (-1)2 − 4(-1) − 4 = 0
f(-1) = 0 ✓ → (x + 1) is a factor
Perform synthetic division by (x + 1):
[1 | 1 | -4 | -4] ÷ (-1) → [1 | 0 | -4]
Quotient: x2 − 4
Factor x^2 − 4:
= (x - 2)(x + 2)
= (x - 2)(x + 1)(x + 2)
(x - 2)(x + 1)(x + 2)
How to factor x^3+x^2-4x-4
To factor x^3+x^2-4x-4, identify the type of polynomial and apply the appropriate technique. The factored form is (x - 2)(x + 1)(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^3+x^2-4x-4?
The answer is (x - 2)(x + 1)(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.