Question

Part A. Let $f(x) = x⁴-3x² + 2$ and $g(x) = 2x⁴ - 6x² + 2x -1$. Let $a$ be a constant.

What is the largest possible degree of $f(x) + a\cdot g(x)$?

Answer 1

The largest possible degree of f(x) + a.g(x) is 8.

Step-by-step explanation:

The largest possible degree of f(x) + a⋅g(x) occurs when the degrees of the two polynomials are added together.

So, we need to find the degree of each polynomial and then add them.

The degree of f(x) = x⁴-3x² + 2 is 4, because 4 is the highest exponent of x.

The degree of g(x) = 2x⁴ - 6x² + 2x -1 is also 4.

Therefore, adding the degrees together, we get a largest possible degree of 4 + 4 = 8.