Question

What value of n makes the equation true? (2x + 4)ⁿ * (4x² + 10) = 8x¹¹ + 20

(A) n = 2
(B) n = 3
(C) n = 4
(D) n = 5

Answer 1

Option B). To make the equation true, n must be 3 so that (2x + 4)^3 provides a 9th degree term that, when multiplied by the quadratic term, results in the 11th degree term 8x^11 in the equation.

Step-by-step explanation:

We need to find a power of n that, when multiplied by the quadratic term 4x2 + 10, gives us an eleventh power term 8x11 as the highest degree in order to solve for n that makes the equation (2x + 4)n * (4x2 + 10) = 8x11 + 20 true. We need the term (2x + 4)n to be of degree 9 in x to reach an x11 term after multiplication since the quadratic term already provides an x2. This is only possible if n = 3. This is because the term 8x9 is obtained from (2x)3, and this term needs to be multiplied by 4x2 to get 8x11.

Therefore, B) n = 3 is the correct answer.