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

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.

x= 149. 24+7=31. 180-31=149

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