Question

1. given the functions (f(x)=2x^{2}-9x - 18) and (g(x)=8x + 12) determine the following. express your answer in simplified form. (3f(x)-4xcdot g(x))

Explanation:

Step1: Multiply \(f(x)\) by 3

First, find \(3f(x)\). Given \(f(x)=2x^{2}-9x - 18\), then \(3f(x)=3(2x^{2}-9x - 18)=6x^{2}-27x-54\).

Step2: Multiply \(x\) and \(g(x)\)

Given \(g(x)=8x + 12\), then \(4x\cdot g(x)=4x(8x + 12)=32x^{2}+48x\).

Step3: Subtract \(4x\cdot g(x)\) from \(3f(x)\)

\(3f(x)-4x\cdot g(x)=(6x^{2}-27x - 54)-(32x^{2}+48x)\)
\(=6x^{2}-27x - 54-32x^{2}-48x\)
\(=(6x^{2}-32x^{2})+(-27x-48x)-54\)
\(=- 26x^{2}-75x-54\)

Answer:

\(-26x^{2}-75x - 54\)