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⋅g(x)?
+532 I assume you may have meant to say smallest, as I have seen those kinds of questions before, so I will answer both.
For largest, because a is a constant, it cannot make the largest exponent any higher, so the answer is 4.
For smallest, we want to cancel some exponents, so we can multiply g(x) by -1/2 and add to get x^4 - 3x^2 + 2 - x^4 + 3x^2 - x + 1/2 = -x + 5/2, so the degree is 1.
Hoping this helped,
asdf334
