Question

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

Answer 1

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 - 4

P = 4: ± 1, 2, 4

Q = 6: ± 1, 2, 3

Possible rational roots are: ± {1, 2, 4, $\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{2}{3}, \dfrac{4}{3}$}

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 factor

The 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 -2

3x(2x + 1)   -2(2x + 1)       So the factors are: (3x - 2) and (2x + 1)