Question

1. perform the following operation (f · g)(x)

$f(x) = 2x^2 - 3x + 5$
$g(x) = 3x - 14$

Explanation:

Step1: Understand the operation

The operation \((f \cdot g)(x)\) means the product of the functions \(f(x)\) and \(g(x)\), so we need to multiply \(f(x) = 2x^2 - 3x + 5\) and \(g(x) = 3x - 14\).

Step2: Multiply the two polynomials

We use the distributive property (FOIL method extended for polynomials):

$$
LATEXBLOCK0
$$

Step3: Combine like terms

Combine the \(x^2\) terms and the \(x\) terms:

$$
LATEXBLOCK1
$$

Answer:

\(6x^3 - 37x^2 + 57x - 70\)