Which of the following are terms In the expansion of 3x 24

Which of the following are terms In the expansion of (3x + 2)^4? Select three that apply. 81x^4 108x^3 Aubrey claims that p(x) = 2x^3 - 6x^2 - 100x + 300 has zeros at 3 and at plusminus k squareroot 2. For the case where Aubrey\'s claim is true, what must be the value of K?

Solution

( 3x + 2)⁴ = 81x⁴ + 216x³ + 216x² + 96x + 16. Thus the 3 terms which appear in ( 3x + 2)⁴ are as under:

A. 81x⁴

C. 216x² and

D 96x

4. p(x) = 2x³ - 6x² - 100x + 300 = 2x² (x -3) - 100(x -3) = (x -3)( 2x² - 100) . Thus the function p(x) has zeros when

(x -3)( 2x² - 100) = 0 i.e. when either x -3 = 0 i.e. when x = 3 or, when 2x² - 100 = 0 or, when x² = 50. i.e.

when x = ± 5 2. . Since as per Aubrey, the zeros of p(x) are at e and   ± k 2 , for Aubrey\'s claim to be true, we must have k = 5.