Composition of polynomials
Let ...

Question

Composition of polynomials

Let ƒ be an nth-degree polynomial and let g be an mth-degree polynomial.

What is the degree of the following polynomials?

ƒ o g

Accepted Answer

Welcome back, everyone. In this problem, we want to determine the degree of the composition of a of x and b of x given that a of x is a yth degree polynomial and b of x is a zed degree polynomial. For our answer choices, a is the product of y and zed, b is y plus zed, c is y divided by zed, and the d is y minus zed. Now, we want to figure out the degree of the composition of a of x and b of x. And since we're talking about the composition of a of x and b of x, we can rewrite it as a of b of x and what that means is that we're putting the function b of x into a of x. But first, we need to figure out what both of them are. The degree of a polynomial is defined as the highest power of a variable in a given polynomial function. In other words, in the function a of x, y is going to be the highest degree of any polynomial in that function. And for B of X, Zed will be the highest degree. So let's say then that a of X. Equals some polynomial x that's raised to the power of y. And let's say that b of x is some polynomial x that's raised to the power of zed. Now we can have we are we can find our composition because that tells us then that a of b of x means we're putting b of x, which is x to the power of zed, into the function a of x, which is x to the power of y. So our function will now become x to the power of zed raised to the power of Y. Now we can apply the rule of exponents here because recall that when we are raising one exponent to another, it's the same thing as multiplying the exponents. Okay. So what that tells us then is that we can rewrite our composition as X to the power of Y multiplied by Z. So that would be the composition of f X and the function b of x. Remember, we want the degree of this composition. And if you look at its degree, if you look at the highest power in this composition, it would have been y zed. Therefore, the degree of our polynomial is y zed, which when we look at our answer choices, would have been answer choice a. Thanks a lot for watching everyone. I hope this video helped.

Composition of polynomials
Let ƒ be an nth-degree polynomial and let g be an mth-degree polynomial.
What is the degree of the following polynomials?
ƒ o g

Key Concepts

Degree of a Polynomial

Composition of Functions

Degree of Composed Polynomials

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