+0

0
304
3

$$\text{Suppose that f is a quadratic polynomial and g is a cubic polynomial, and both f and g have a leading coefficient of 1. What is the maximum degree of the polynomial (f(x))^3 - (g(x))^2 + f(x) - 1? }$$

Jul 19, 2019

#2
+507
+2

Because both the leading coefficients of f(x) and g(x) are 1, the x^6 term would cancel out, giving a maximum degree of 5.

Jul 19, 2019
#3
+111387
+3

Let g(x)  =  x^3 + x^2

Let f(x) be  x^2 + x

Note that....in both cases.....the lead coefficient is "1"

So....we have that

[ x^2 + x]^3  -  [ x^3 + x^2 ]^2 + [x^2 + x ] - 1     =

x^5 + 2 x^4 + x^3 + x^2 + x - 1

So.....as Davis found....the max degree is  5

Jul 19, 2019