Based on the polynomial remainder theorem, what is the value of the function when x = 3? f(x)=x4+3x3−6x2−12x−8

64

Step-by-step explanation:

Evaluate x^4 + 3 x^3 - 6 x^2 - 12 x - 8 where x = 3:

x^4 + 3 x^3 - 6 x^2 - 12 x - 8 = 3^4 + 3×3^3 - 6×3^2 - 12×3 - 8

3^3 = 3×3^2:

3^4 + 3×3×3^2 - 6×3^2 - 12×3 - 8

3^2 = 9:

3^4 + 3×3×9 - 6×3^2 - 12×3 - 8

3×9 = 27:

3^4 + 3×27 - 6×3^2 - 12×3 - 8

3^2 = 9:

3^4 + 3×27 - 69 - 12×3 - 8

3^4 = (3^2)^2:

(3^2)^2 + 3×27 - 6×9 - 12×3 - 8

3^2 = 9:

9^2 + 3×27 - 6×9 - 12×3 - 8

9^2 = 81:

81 + 3×27 - 6×9 - 12×3 - 8

3×27 = 81:

81 + 81 - 6×9 - 12×3 - 8

-6×9 = -54:

81 + 81 + -54 - 12×3 - 8

-12×3 = -36:

81 + 81 - 54 + -36 - 8

81 + 81 - 54 - 36 - 8 = (81 + 81) - (54 + 36 + 8):

(81 + 81) - (54 + 36 + 8)

| 8 | 1

+ | 8 | 1

1 | 6 | 2:

162 - (54 + 36 + 8)

| 1 |  

| 5 | 4

| 3 | 6

+ | | 8

| 9 | 8:

162 - 98

| | 15 |  

| 0 | 5 | 12

| 1 | 6 | 2

- | | 9 | 8

| 0 | 6 | 4:

 64

answer: there are 453.592 grams in a pound.

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.