Which of the following polynomials can approximate the expression (4x3+5)(3x6−8x2)2x2+8x−4+4x3−2x+13?(1 point)

12x7−27

6x7+15

6x7+13

6x7−7

1 answer

To determine which polynomial can approximate the given expression, we need to multiply the expressions (4x^3+5) and (3x^6−8x^2), and then multiply the result by 2x^2+8x−4. Finally, add 4x^3−2x+13.

First, multiply (4x^3+5) and (3x^6−8x^2):
(4x^3+5)(3x^6−8x^2) = 12x^9−32x^5+15x^6−40x^2

Next, multiply the result by 2x^2+8x−4:
(2x^2+8x−4)(12x^9−32x^5+15x^6−40x^2) = 24x^11−64x^7+30x^8−80x^4+96x^10−256x^6+120x^7−320x^3−48x^9+128x^5−60x^6+160x^2

Finally, add 4x^3−2x+13 to the result:
24x^11−64x^7+30x^8−80x^4+96x^10−256x^6+120x^7−320x^3−48x^9+128x^5−60x^6+160x^2+4x^3−2x+13 = 24x^11−48x^9−14x^8−176x^7+68x^6−128x^5−320x^3+160x^2−2x+13

From the given options, the closest polynomial to this expression is 24x^11−48x^9−14x^8−176x^7+68x^6−128x^5−320x^3+160x^2−2x+13.

Therefore, the answer is not among the given options.