Question

When 36x⁴ + 12x⁸ is ÷ by 12x⁴, the result is _?

A. 3 + 12x⁴
B. 3 + 12x⁶
C. 3 + x⁴
D. 3x + x²

Answer 1

Dividing the given expression by 12x⁴ results in simplifying each term individually, with the first term simplifying to 3 and the second to x⁴. The final simplified expression is 3 + x⁴.

Step-by-step explanation:

When the expression 36x⁴ + 12x⁸ is divided by 12x⁴, we can divide each term separately to simplify the expression. Here's how it's done step-by-step:

1. Divide the first term 36x⁴ by 12x⁴. The coefficient 36 divided by 12 is 3, and since the variables are the same with equal exponents, they divide out to 1. So, this term simplifies to 3.
2. Next, divide the second term 12x⁸ by 12x⁴. The coefficient 12 divided by 12 is 1, and subtracting the exponents (as per the division rule of exponents) gives us x⁸ - x⁴ = x⁴. So, this term simplifies to x⁴.
3. Write out the simplified expression as 3 + x⁴.

Therefore, when 36x⁴ + 12x⁸ is divided by 12x⁴, the result is 3 + x⁴ (option C).