What is 3[f(x + 2)] if f(x) = x^3 + 2x^2 - 4?

Question

What is 3[f(x + 2)] if f(x) = x^3 + 2x^2 - 4?

Answer 1

x=4

Answer 2

What is 3[f(x + 2)] if f(x) = x^3 + 2x^2 - 4?

(1) apply this given f(x + 2) in term of x into equation:

      = (x+2)^3 + 2(x+2)^2 - 4

(2) Expand the terms by special products first; then, multiply the constant/coefficient of 3. You will get the answer. 3 [(x+2)^3 + 2(x+2)^2 - 4]

Here is how:

= 3[(x^3+3x^2(2)+3x(2)^2+8) + 2(x^2+4x+4)-4]

= 3 [ x^3+6x^2+12x+8 + 2x^2+8x+8-4]

= [3x^3+18x^2+36x+24 + 6x^2+24x+12]

= 3x^3+24x^2+60x+36

Hope it helps.

W.

Answer 3

first, substitute x = x+2 into the original equation of f(x):

f(x+2) = (x+2)^3 + 2(x+2)^2 - 4

expand this expand and combine like terms:

= (x+2)(x+2)(x+2) + 2(x+2)(x+2) - 4 = x^3 + 6x^2 + 12x +8 + 2(x^2 + 4x+ 4) - 4 = x^3 + 6x^2 + 12x +8 + 2x^2 + 8x+ 8 - 4 = x^3 + 8x^2 + 20x +12

finally, multiply the entire f(x+2) by 3 to get the final result:

3[f(x+2)] = 3[x^3 + 8x^2 + 20x +12] = 3x^3 + 24x^2 + 60x + 36

Answer 4

note

3[f(x + 2)] if f(x) = x^3 + 2x^2 - 4

f(x + 2) = (x + 2)^3 + 2(x + 2)^2 - 4

so

3[f(x + 2)] =

3[(x + 2)^3 + 2(x + 2)^2 - 4] =

3[x^3 + 4x^2 + 8x + 8 + 2(x^2 + 2x + 4) - 4] =

3[x^3 + 4x^2 + 8x + 8 + 2x^2 + 4x + 8 - 4] =

3[x^3 + 6x^2 + 12x + 12] =

3x^3 + 18x^2 + 36x + 36