What is the degree of the polynomial resulting from g(f(x)) when f(x) = 2x + 3 and g(x) = x^2?

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Multiple Choice

What is the degree of the polynomial resulting from g(f(x)) when f(x) = 2x + 3 and g(x) = x^2?

Explanation:
The degree of a composition of polynomials is the product of their degrees when the inner polynomial has positive degree. Here the inner function f(x) = 2x + 3 is linear, so its degree is 1. The outer function g(x) = x^2 has degree 2. Therefore the composition g(f(x)) has degree 2 × 1 = 2. If you expand it, g(f(x)) = (2x + 3)^2 = 4x^2 + 12x + 9, which indeed is a quadratic. So the resulting degree is 2.

The degree of a composition of polynomials is the product of their degrees when the inner polynomial has positive degree. Here the inner function f(x) = 2x + 3 is linear, so its degree is 1. The outer function g(x) = x^2 has degree 2. Therefore the composition g(f(x)) has degree 2 × 1 = 2. If you expand it, g(f(x)) = (2x + 3)^2 = 4x^2 + 12x + 9, which indeed is a quadratic. So the resulting degree is 2.

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