Rational root theorem

Question

Use the rational root theorem to identify the possible roots. Verify with synthetic division and write as a product of its factors. Use the factors to find the remaining roots. Use additional paper for your work.

h(x)=x^3+3x^2-4x-12

Answer 1

List of possible rational zeros: ±1, ±2, ±3, ±4, ±6, ±12.

x = 2 from this list and h(2) = 0

2 I 1 3 -4 -12

2 10 12

1 5 6 0

Quotient x² + 5x + 6 = 0; x = -2 or x = -3

Unswer: {-2, -3, 2}