Problem

Given two functions, \(f(x) = 3x^2 + 2x - 1\) and \(g(x) = x^2 - 4\). Find the sum and the product of the two functions.

Answer

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Answer

Step 5: Combine like terms. \(f(x) \cdot g(x) = 3x^4 + 2x^3 - 13x^2 - 8x + 4\)

Steps

Step 1 ：Step 1: Find the sum of the two functions. \(f(x) + g(x) = (3x^2 + 2x - 1) + (x^2 - 4)\)

Step 2 ：Step 2: Combine like terms. \(f(x) + g(x) = 4x^2 + 2x - 5\)

Step 3 ：Step 3: Find the product of the two functions. \(f(x) \cdot g(x) = (3x^2 + 2x - 1) \cdot (x^2 - 4)\)

Step 4 ：Step 4: Distribute each term in the first function to each term in the second function. \(f(x) \cdot g(x) = 3x^4 - 12x^2 + 2x^3 - 8x - x^2 + 4\)

Step 5 ：Step 5: Combine like terms. \(f(x) \cdot g(x) = 3x^4 + 2x^3 - 13x^2 - 8x + 4\)

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