6x^3+11x^2-4x-4 divide the polynomial

Answer:   (x + 2)(3x - 2)(2x + 1)Step-by-step explanation:First, find the possible rational roots. Then use synthetic division (or long division) to find a root. Next, factor the reduced polynomial.6x³ + 11x² - 4x - 4P = 4: ± 1, 2, 4Q = 6: ± 1, 2, 3 Possible rational roots are: ± {1, 2, 4, [tex]\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{2}{3}, \dfrac{4}{3}[/tex]}Try x = -2   -->   which is the factor (x + 2)-2 |  6    11   -4    -4    |   ↓  -12   2     4         6    -1   -2     0   ← Remainder of 0 means (x + 2) is a factorThe reduced polynomial is:      6x² - 1x - 2            Factors of (6)(-2) = -12                                ∧                              1 -12 = -11                              2 -6 = -4                              3 -4 = -1   this works!Replace -1x with +3x - 4x and use the grouping method to factor:   6x² + 3x  -4x -23x(2x + 1)   -2(2x + 1)       So the factors are: (3x - 2) and (2x + 1)