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

  (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, }

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)

correct answer is b. 27/8

step-by-step explanation:

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!